Analysis and Design of Singular Markovian Jump Systems

This monograph is an up-to-date presentation of the analysis and design of singular Markovian jump systems (SMJSs) in which the transition rate matrix of the underlying systems is generally uncertain, partially unknown and designed. The problems addressed include stability, stabilization, H? control and filtering, observer design, and adaptive control. applications of Markov process are investigated by using Lyapunov theory, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat’s Lemma, among other techniques. Features of the book include: · study of the stability problem for SMJSs with general transition rate matrices (TRMs); · stabilization for SMJSs by TRM design, noise control, proportional-derivative and partially mode-dependent control, in terms of LMIs with and without equation constraints; · mode-dependent and mode-independent H? control solutions with development of a type of disordered controller; · observer-based controllers of SMJSs in which both the designed observer and controller are either mode-dependent or mode-independent; · consideration of robust H? filtering in terms of uncertain TRM or filter parameters leading to a method for totally mode-independent filtering · development of LMI-based conditions for a class of adaptive state feedback controllers with almost-certainly-bounded estimated error and almost-certainly-asymptotically-stable corresponding closed-loop system states · applications of Markov process on singular systems with norm bounded uncertainties and time-varying delays Analysis and Design of Singular Markovian Jump Systems contains valuable reference material for academic researchers wishing to explore the area. The contents are also suitable for a one-semester graduate course

Robust controller design for input-delayed systems using predictive feedback and an uncertainty estimator

[EN] This paper deals with the problem of stabilizing a class of input-delayed systems with (possibly) nonlinear uncertainties by using explicit delay compensation. It is well known that plain predictive schemes lack robustness with respect to uncertain model parameters. In this work, an uncertainty estimator is derived for input-delay systems and combined with a modified state predictor, which uses current available information of the estimated uncertainties. Furthermore, based on Lyapunov-Krasovskii functionals, a computable criterion to check robust stability of the closed-loop is developed and cast into a minimization problem constrained to an LMI. Additionally, for a given input delay, an iterative-LMI algorithm is proposed to design stabilizing tuning parameters. The main results are illustrated and validated using a numerical example with a second-order dynamic system.This work was partially supported by projects PROMETEOII/2013/004, Conselleria d Educació, Generalitat Valenciana, and TIN2014-56158-C4-4-P-AR, Ministerio de Economía y Competitividad, Spain.Sanz Diaz, R.; García Gil, PJ.; Albertos Pérez, P.; Zhong, Q. (2017). Robust controller design for input-delayed systems using predictive feedback and an uncertainty estimator. International Journal of Robust and Nonlinear Control. 27(10):1826-1840. https://doi.org/10.1002/rnc.3639S182618402710Stability and Stabilization of Systems with Time Delay. (2011). IEEE Control Systems, 31(1), 38-65. doi:10.1109/mcs.2010.939135Normey-Rico, J. E., Bordons, C., & Camacho, E. F. (1997). Improving the robustness of dead-time compensating PI controllers. Control Engineering Practice, 5(6), 801-810. doi:10.1016/s0967-0661(97)00064-6Michiels, W., & Niculescu, S.-I. (2003). On the delay sensitivity of Smith Predictors. International Journal of Systems Science, 34(8-9), 543-551. doi:10.1080/00207720310001609057Normey-Rico, J. E., & Camacho, E. F. (2008). Dead-time compensators: A survey. Control Engineering Practice, 16(4), 407-428. doi:10.1016/j.conengprac.2007.05.006Guzmán, J. L., García, P., Hägglund, T., Dormido, S., Albertos, P., & Berenguel, M. (2008). Interactive tool for analysis of time-delay systems with dead-time compensators. Control Engineering Practice, 16(7), 824-835. doi:10.1016/j.conengprac.2007.09.002Manitius, A., & Olbrot, A. (1979). Finite spectrum assignment problem for systems with delays. IEEE Transactions on Automatic Control, 24(4), 541-552. doi:10.1109/tac.1979.1102124Artstein, Z. (1982). Linear systems with delayed controls: A reduction. IEEE Transactions on Automatic Control, 27(4), 869-879. doi:10.1109/tac.1982.1103023Moon, Y. S., Park, P., & Kwon, W. H. (2001). Robust stabilization of uncertain input-delayed systems using reduction method. Automatica, 37(2), 307-312. doi:10.1016/s0005-1098(00)00145-xYue, D. (2004). Robust stabilization of uncertain systems with unknown input delay. Automatica, 40(2), 331-336. doi:10.1016/j.automatica.2003.10.005Yue, D., & Han, Q.-L. (2005). Delayed feedback control of uncertain systems with time-varying input delay. Automatica, 41(2), 233-240. doi:10.1016/j.automatica.2004.09.006Lozano, R., Castillo, P., Garcia, P., & Dzul, A. (2004). Robust prediction-based control for unstable delay systems: Application to the yaw control of a mini-helicopter. Automatica, 40(4), 603-612. doi:10.1016/j.automatica.2003.10.007Gonzalez, A., Garcia, P., Albertos, P., Castillo, P., & Lozano, R. (2012). Robustness of a discrete-time predictor-based controller for time-varying measurement delay. Control Engineering Practice, 20(2), 102-110. doi:10.1016/j.conengprac.2011.09.001Karafyllis, I., & Krstic, M. (2013). Robust predictor feedback for discrete-time systems with input delays. International Journal of Control, 86(9), 1652-1663. doi:10.1080/00207179.2013.792005Krstic, M. (2010). Input Delay Compensation for Forward Complete and Strict-Feedforward Nonlinear Systems. IEEE Transactions on Automatic Control, 55(2), 287-303. doi:10.1109/tac.2009.2034923Bekiaris-Liberis, N., & Krstic, M. (2011). Compensation of Time-Varying Input and State Delays for Nonlinear Systems. Journal of Dynamic Systems, Measurement, and Control, 134(1). doi:10.1115/1.4005278Karafyllis, I., Malisoff, M., Mazenc, F., & Pepe, P. (Eds.). (2016). Recent Results on Nonlinear Delay Control Systems. Advances in Delays and Dynamics. doi:10.1007/978-3-319-18072-4Cacace, F., Conte, F., Germani, A., & Pepe, P. (2016). Stabilization of strict-feedback nonlinear systems with input delay using closed-loop predictors. International Journal of Robust and Nonlinear Control, 26(16), 3524-3540. doi:10.1002/rnc.3517Fridman, E., & Shaked, U. (2002). An improved stabilization method for linear time-delay systems. IEEE Transactions on Automatic Control, 47(11), 1931-1937. doi:10.1109/tac.2002.804462Fridman, E., & Shaked, U. (2002). A descriptor system approach to H/sub ∞/ control of linear time-delay systems. IEEE Transactions on Automatic Control, 47(2), 253-270. doi:10.1109/9.983353Chen, W.-H., & Zheng, W. X. (2006). On improved robust stabilization of uncertain systems with unknown input delay. Automatica, 42(6), 1067-1072. doi:10.1016/j.automatica.2006.02.015Krstic, M. (2008). Lyapunov tools for predictor feedbacks for delay systems: Inverse optimality and robustness to delay mismatch. Automatica, 44(11), 2930-2935. doi:10.1016/j.automatica.2008.04.010Léchappé, V., Moulay, E., Plestan, F., Glumineau, A., & Chriette, A. (2015). New predictive scheme for the control of LTI systems with input delay and unknown disturbances. Automatica, 52, 179-184. doi:10.1016/j.automatica.2014.11.003Roh, Y.-H., & Oh, J.-H. (1999). Robust stabilization of uncertain input-delay systems by sliding mode control with delay compensation. Automatica, 35(11), 1861-1865. doi:10.1016/s0005-1098(99)00106-5Bresch-Pietri, D., & Krstic, M. (2009). Adaptive trajectory tracking despite unknown input delay and plant parameters. Automatica, 45(9), 2074-2081. doi:10.1016/j.automatica.2009.04.027Kamalapurkar, R., Fischer, N., Obuz, S., & Dixon, W. E. (2016). Time-Varying Input and State Delay Compensation for Uncertain Nonlinear Systems. IEEE Transactions on Automatic Control, 61(3), 834-839. doi:10.1109/tac.2015.2451472Chen, W.-H., Ohnishi, K., & Guo, L. (2015). Advances in Disturbance/Uncertainty Estimation and Attenuation [Guest editors’ introduction]. IEEE Transactions on Industrial Electronics, 62(9), 5758-5762. doi:10.1109/tie.2015.2453347Chen, W.-H., Yang, J., Guo, L., & Li, S. (2016). Disturbance-Observer-Based Control and Related Methods—An Overview. IEEE Transactions on Industrial Electronics, 63(2), 1083-1095. doi:10.1109/tie.2015.2478397Sariyildiz E Ohnishi K Design constraints of disturbance observer in the presence of time delay 2013 IEEE International Conference on Mechatronics (ICM) Vicenza, Italy 2013 69 74Wang, Q.-G., Hang, C. C., & Yang, X.-P. (2001). Single-loop controller design via IMC principles. Automatica, 37(12), 2041-2048. doi:10.1016/s0005-1098(01)00170-4Zheng, Q., & Gao, Z. (2014). Predictive active disturbance rejection control for processes with time delay. ISA Transactions, 53(4), 873-881. doi:10.1016/j.isatra.2013.09.021Chen, M., & Chen, W.-H. (2010). Disturbance-observer-based robust control for time delay uncertain systems. International Journal of Control, Automation and Systems, 8(2), 445-453. doi:10.1007/s12555-010-0233-5Guo, L., & Chen, W.-H. (2005). Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach. International Journal of Robust and Nonlinear Control, 15(3), 109-125. doi:10.1002/rnc.978Zhong, Q.-C., & Rees, D. (2004). Control of Uncertain LTI Systems Based on an Uncertainty and Disturbance Estimator. Journal of Dynamic Systems, Measurement, and Control, 126(4), 905-910. doi:10.1115/1.1850529Yong He, Min Wu, & Jin-Hua She. (2005). Improved bounded-real-lemma representation and H/sub /spl infin// control of systems with polytopic uncertainties. IEEE Transactions on Circuits and Systems II: Express Briefs, 52(7), 380-383. doi:10.1109/tcsii.2005.850418CAO, Y.-Y., LAM, J., & SUN, Y.-X. (1998). Static Output Feedback Stabilization: An ILMI Approach. Automatica, 34(12), 1641-1645. doi:10.1016/s0005-1098(98)80021-6Marler, R. T., & Arora, J. S. (2009). The weighted sum method for multi-objective optimization: new insights. Structural and Multidisciplinary Optimization, 41(6), 853-862. doi:10.1007/s00158-009-0460-7Fridman, E. (2014). Introduction to Time-Delay Systems. Systems & Control: Foundations & Applications. doi:10.1007/978-3-319-09393-2Solomon, O., & Fridman, E. (2013). New stability conditions for systems with distributed delays. Automatica, 49(11), 3467-3475. doi:10.1016/j.automatica.2013.08.025Huaizhong Li, & Minyue Fu. (1997). A linear matrix inequality approach to robust H/sub ∞/ filtering. IEEE Transactions on Signal Processing, 45(9), 2338-2350. doi:10.1109/78.622956Šiljak, D. D., & Stipanovic, D. M. (2000). Robust stabilization of nonlinear systems: The LMI approach. Mathematical Problems in Engineering, 6(5), 461-493. doi:10.1155/s1024123x0000143

Robustness analysis of discrete predictor-based controllers for input-delay systems

In this article, robustness to model uncertainties are analysed in the context of discrete predictor-based state-feedback controllers for discrete-time input-delay systems with time-varying delay, in an LMI framework. The goal is comparing robustness of predictor-based strategies with respect to other (sub)optimal state feedback ones. A numerical example illustrates that improvements in tolerance to modelling errors can be achieved by using the predictor framework.The authors are grateful for grant nos. DPI2008-06737-C02-01, DPI2008-06731-C02-01, DPI2011-27845-C02-01 and PROMETEO/2008/088 from the Spanish and Valencian governments.González Sorribes, A.; Sala, A.; García Gil, PJ.; Albertos Pérez, P. (2013). Robustness analysis of discrete predictor-based controllers for input-delay systems. International Journal of Systems Science. 44(2):232-239. https://doi.org/10.1080/00207721.2011.600469S232239442Boukas, E.-K. (2006). Discrete-time systems with time-varying time delay: Stability and stabilizability. Mathematical Problems in Engineering, 2006, 1-10. doi:10.1155/mpe/2006/42489Du, D., Jiang, B., & Zhou, S. (2008). Delay-dependent robust stabilisation of uncertain discrete-time switched systems with time-varying state delay. International Journal of Systems Science, 39(3), 305-313. doi:10.1080/00207720701805982El Ghaoui, L., Oustry, F., & AitRami, M. (1997). A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Transactions on Automatic Control, 42(8), 1171-1176. doi:10.1109/9.618250Gao, H., & Chen, T. (2007). New Results on Stability of Discrete-Time Systems With Time-Varying State Delay. IEEE Transactions on Automatic Control, 52(2), 328-334. doi:10.1109/tac.2006.890320Gao, H., Wang, C., Lam, J., & Wang, Y. (2004). Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay. IEE Proceedings - Control Theory and Applications, 151(6), 691-698. doi:10.1049/ip-cta:20040822Gao, H., Chen, T., & Lam, J. (2008). A new delay system approach to network-based control. Automatica, 44(1), 39-52. doi:10.1016/j.automatica.2007.04.020Garcia , P , Castillo , P , Lozano , R and Albertos , P . 2006 . Robustness with Respect to Delay Uncertainties of a Predictor Observer Based Discrete-time Controller . Proceeding of the 45th IEEE Conference on Decision and Control . 2006 . pp. 199 – 204 .Guo , Y and Li , S . 2009 . New Stability Criterion for Discrete-time Systems with Interval Time-varying State Delay . Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference . 2009 . pp. 1342 – 1347 .Hägglund, T. (1996). An industrial dead-time compensating PI controller. Control Engineering Practice, 4(6), 749-756. doi:10.1016/0967-0661(96)00065-2V.J.S. Leite, and Miranda, M.F. (2008), ‘Robust Stabilization of Discrete-time Systems with Time-varying Delay: An LMI Approach’,Mathematical Problems in Engineering, 2008, 15 pages (doi:10.1155/2008/875609)Liu, X. G., Tang, M. L., Martin, R. R., & Wu, M. (2006). Delay-dependent robust stabilisation of discrete-time systems with time-varying delay. IEE Proceedings - Control Theory and Applications, 153(6), 689-702. doi:10.1049/ip-cta:20050223Lozano, R., Castillo, P., Garcia, P., & Dzul, A. (2004). Robust prediction-based control for unstable delay systems: Application to the yaw control of a mini-helicopter. Automatica, 40(4), 603-612. doi:10.1016/j.automatica.2003.10.007Manitius, A., & Olbrot, A. (1979). Finite spectrum assignment problem for systems with delays. IEEE Transactions on Automatic Control, 24(4), 541-552. doi:10.1109/tac.1979.1102124Michiels, W., & Niculescu, S.-I. (2003). On the delay sensitivity of Smith Predictors. International Journal of Systems Science, 34(8-9), 543-551. doi:10.1080/00207720310001609057Palmor, Z.J. (1996), ‘Time-delay Compensation – Smith Predictor and Its Modifications’, inThe Control Handbook, ed. W.S. Levine, Boca Raton: CRC Press, pp. 224–237Pan, Y.-J., Marquez, H. J., & Chen, T. (2006). Stabilization of remote control systems with unknown time varying delays by LMI techniques. International Journal of Control, 79(7), 752-763. doi:10.1080/00207170600654554Richard, J.-P. (2003). Time-delay systems: an overview of some recent advances and open problems. Automatica, 39(10), 1667-1694. doi:10.1016/s0005-1098(03)00167-5Wang, Q.-G., Lee, T. H., & Tan, K. K. (1999). Finite-Spectrum Assignment for Time-Delay Systems. Lecture Notes in Control and Information Sciences. doi:10.1007/978-1-84628-531-8He, Y., Wu, M., Han, Q.-L., & She, J.-H. (2008). Delay-dependentH∞control of linear discrete-time systems with an interval-like time-varying delay. International Journal of Systems Science, 39(4), 427-436. doi:10.1080/00207720701832531Yue, D., & Han, Q.-L. (2005). Delayed feedback control of uncertain systems with time-varying input delay. Automatica, 41(2), 233-240. doi:10.1016/j.automatica.2004.09.006Zhang, B., Xu, S., & Zou, Y. (2008). Improved stability criterion and its applications in delayed controller design for discrete-time systems. Automatica, 44(11), 2963-2967. doi:10.1016/j.automatica.2008.04.01

A non-uniform predictor-observer for a networked control system

The final publication is available at Springer via http://dx.doi.org/10.1007/s12555-011-0621-5This paper presents a Non-Uniform Predictor-Observer (NUPO) based control approach in order to deal with two of the main problems related to Networked Control Systems (NCS) or Sensor Networks (SN): time-varying delays and packet loss. In addition, if these delays are longer than the sampling period, the packet disordering phenomenon can appear. Due to these issues, a (scarce) nonuniform, delayed measurement signal could be received by the controller. But including the NUPO proposal in the control system, the delay will be compensated by the prediction stage, and the nonavailable data will be reconstructed by the observer stage. So, a delay-free, uniformly sampled controller design can be adopted. To ensure stability, the predictor must satisfy a feasibility problem based on a time-varying delay-dependent condition expressed in terms of Linear Matrix Inequalities (LMI). Some aspects like the relation between network delay and robustness/performance trade-off are empirically studied. A simulation example shows the benefits (robustness and control performance improvement) of the NUPO approach by comparison to another similar proposal. © ICROS, KIEE and Springer 2011.This work was supported by the Spanish Ministerio de Ciencia y Tecnologia Projects DPI2008-06737-C02-01 and DPI2009-14744-C03-03, by Generalitat Valenciana Project GV/2010/018, by Universidad Politecnica de Valencia Project PAID06-08.Cuenca Lacruz, ÁM.; García Gil, PJ.; Albertos Pérez, P.; Salt Llobregat, JJ. (2011). A non-uniform predictor-observer for a networked control system. International Journal of Control, Automation and Systems. 9(6):1194-1202. doi:10.1007/s12555-011-0621-5S1194120296K. Ogata, Discrete-time Control Systems, Prentice-Hall, Inc., Upper Saddle River, NJ, USA, 1987.Y. Tipsuwan and M. Chow, “Control methodologies in networked control systems,” Control Eng. Practice, vol. 11, no. 10, pp. 1099–1111, 2003.T. Jia, Y. Niu, and X. Wang, “H ∞ control for networked systems with data packet dropout,” Int. J. Control, Autom., and Syst., vol. 8, no. 2, pp. 198–203, 2010.Y. Wang and G. Yang, “Robust H ∞ model reference tracking control for networked control systems with communication constraints,” Int. J. Control, Autom., and Syst., vol. 7, no. 6, pp. 992–1000, 2009.H. Gao and T. Chen, “Network-based H ∞ output tracking control,” IEEE Trans. Autom. Control, vol. 53, no. 3, pp. 655–667, 2008.H. Karimi, “Robust H ∞ filter design for uncertain linear systems over network with network-induced delays and output quantization,” Modeling, Identification and Control, vol. 30, no. 1, pp. 27–37, 2009.H. R. Karimi, “Delay-range-dependent linear matrix inequality approach to quantized H ∞ control of linear systems with network-induced delays and norm-bounded uncertainties,” Proc. of the Inst. of Mech. Eng., Part I: J. of Syst. and Control Eng., vol. 224, no. 6, pp. 689–700, 2010.K. Lee, S. Lee, and M. Lee, “Remote fuzzy logic control of networked control system via Profibus-DP,” IEEE Trans. Ind. Electron., vol. 50, no. 4, pp. 784–792, 2003.Y. Tipsuwan and M.-Y. Chow, “Gain scheduler middleware: a methodology to enable existing controllers for networked control and teleoperationpart I: networked Control,” IEEE Trans. on Industrial Electronics, vol. 51, no. 6, pp. 1218–1227, December 2004.A. Sala, A. Cuenca, and J. Salt, “A retunable PID multi-rate controller for a networked control system,” Inform. Sci., vol. 179, no. 14, pp. 2390–2402, June 2009.A. Cuenca, J. Salt, V. Casanova, and R. Piza, “An approach based on an adaptive multi-rate Smith predictor and gain scheduling for a networked control system: implementation over Profibus-DP,” Int. J. Control, Autom., and Syst., vol. 8, no. 2, pp. 473–481, April 2010.A. Cuenca, J. Salt, A. Sala, and R. Piza, “A delay-dependent dual-rate PID controller over an Ethernet network,” IEEE Trans. Ind. Informat., vol. 7, no. 1, pp. 18–29, Feb. 2011.Y. Tian and D. Levy, “Compensation for control packet dropout in networked control systems,” Inform. Sci., vol. 178, no. 5, pp. 1263–1278, 2008.Y. Zhao, G. Liu, and D. Rees, “Modeling and stabilization of continuous-time packet-based networked control systems.” IEEE Trans. Syst., Man, Cybern. B, vol. 39, no. 6, pp. 1646–1652, Dec. 2009.X. Zhao, S. Fei, and C. Sun, “Impulsive controller design for singular networked control systems with packet dropouts,” Int. J. Control, Autom., and Syst., vol. 7, no. 6, pp. 1020–1025, 2009.H. Gao and T. Chen, “H ∞ estimation for uncertain systems with limited communication capacity,” IEEE Trans. Autom. Control, vol. 52, no. 11, pp. 2070–2084, 2007.S. Oh, L. Schenato, P. Chen, and S. Sastry, “Tracking and coordination of multiple agents using sensor networks: System design, algorithms and experiments,” Proc. of the IEEE, vol. 95, no. 1, pp. 234–254, 2007.M. Moayedi, Y. Foo, and Y. Soh, “Optimal and suboptimal minimum-variance filtering in networked systems with mixed uncertainties of random sensor delays, packet dropouts and missing measurements,” Int. J. Control, Autom., and Syst., vol. 8, no. 6, pp. 1179–1188, 2010.W. Zhang, M. Branicky, and S. Phillips, “Stability of networked control systems,” IEEE Control Syst. Mag., vol. 21, no. 1, pp. 84–99, 2001.J. Hespanha, P. Naghshtabrizi, and Y. Xu, “A survey of recent results in networked control systems,” Proc. of the IEEE, vol. 95, no. 1, pp. 138–162, 2007.J. Baillieul and P. Antsaklis, “Control and communication challenges in networked real-time systems,” Proc. of the IEEE, vol. 95, no. 1, pp. 9–28, 2007.P. Garcia, P. Castillo, R. Lozano, and P. Albertos, “Robustness with respect to delay uncertainties of a predictor-observer based discrete-time controller,” Proc. of the 45th IEEE Conf. on Decision and Control, pp. 199–204, 2006.C. Lien, “Robust observer-based control of systems with state perturbations via LMI approach,” IEEE Trans. Autom. Control, vol. 49, no. 8, pp. 1365–1370, 2004.A. Sala, “Computer control under time-varying sampling period: an LMI gridding approach,” Automatica, vol. 41, no. 12, pp. 2077–2082, Dec. 2005.J. Li, Q. Zhang, Y. Wang, and M. Cai, “H ∞ control of networked control systems with packet disordering,” IET Control Theory Appl., vol. 3, no. 11, pp. 1463–1475, March 2009.Y. Zhao, G. Liu, and D. Rees, “Improved predictive control approach to networked control systems,” IET Control Theory Appl., vol. 2, no. 8, pp. 675–681, Aug. 2008.K. Astrom, “Event based control,” Analysis and Design of Nonlinear Control Systems, pp. 127–147, 2007.A. Cuenca, P. García, K. Arzén, and P. Albertos, “A predictor-observer for a networked control system with time-varying delays and non-uniform sampling,” Proc. Eur. Control Conf., pp. 946–951, 2009.J. Xiong and J. Lam, “Stabilization of linear systems over networks with bounded packet loss,” Automatica, vol. 43, no. 1, pp. 80–87, 2007.H. Song, L. Yu, and A. Liu, “H ∞ filtering for network-based systems with communication constraints and packet dropouts,” Proc. of the 7th Asian Control Conf., pp. 220–225, 2009.P. Garcia, A. Gonzalez, P. Castillo, R. Lozano, and P. Albertos, “Robustness of a discrete-time predictor-based controller for time-varying measurement delay,” Proc. of the 9th IFAC Workshop on Time Delay Systems, 2010.J. Sturm, “Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones,” Optimization methods and software, vol. 11, no. 1, pp. 625–653, 1999.T. Henningsson and K. Astrom, “Log-concave observers,” Proc. of the 17th Int. Symp. on Mathematical Theory of Networks and Systems, pp. 2163–2170, 2006.D. Davison and E. Hwang, “Automating radiotherapy cancer treatment: use of multirate observer-based control,” Proc. of American Control Conf., vol. 2, pp. 1194–1199, 2003

Memory Resilient Gain-scheduled State-Feedback Control of Uncertain LTI/LPV Systems with Time-Varying Delays

The stabilization of uncertain LTI/LPV time delay systems with time varying delays by state-feedback controllers is addressed. At the difference of other works in the literature, the proposed approach allows for the synthesis of resilient controllers with respect to uncertainties on the implemented delay. It is emphasized that such controllers unify memoryless and exact-memory controllers usually considered in the literature. The solutions to the stability and stabilization problems are expressed in terms of LMIs which allow to check the stability of the closed-loop system for a given bound on the knowledge error and even optimize the uncertainty radius under some performance constraints; in this paper, the $\mathcal{H}_\infty$ performance measure is considered. The interest of the approach is finally illustrated through several examples

Robust H∞ filtering for a class of nonlinear networked systems with multiple stochastic communication delays and packet dropouts

Copyright [2010] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the robust H∞ filtering problem is studied for a class of uncertain nonlinear networked systems with both multiple stochastic time-varying communication delays and multiple packet dropouts. A sequence of random variables, all of which are mutually independent but obey Bernoulli distribution, are introduced to account for the randomly occurred communication delays. The packet dropout phenomenon occurs in a random way and the occurrence probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution in the interval. The discrete-time system under consideration is also subject to parameter uncertainties, state-dependent stochastic disturbances and sector-bounded nonlinearities. We aim to design a linear full-order filter such that the estimation error converges to zero exponentially in the mean square while the disturbance rejection attenuation is constrained to a give level by means of the H∞ performance index. Intensive stochastic analysis is carried out to obtain sufficient conditions for ensuring the exponential stability as well as prescribed H∞ performance for the overall filtering error dynamics, in the presence of random delays, random dropouts, nonlinearities, and the parameter uncertainties. These conditions are characterized in terms of the feasibility of a set of linear matrix inequalities (LMIs), and then the explicit expression is given for the desired filter parameters. Simulation results are employed to demonstrate the effectiveness of the proposed filter design technique in this paper.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the Alexander von Humboldt Foundation of Germany, National Natural Science Foundation of China under Grant 60825303, 60834003, 973 Project under Grant 2009CB320600, Fok Ying Tung Education Foundation under Grant 111064, and the Youth Science Fund of Heilongjiang Province under Grant QC2009C63

Robust moving horizon H∞ control of discrete time-delayed systems with interval time-varying delays

In this study, design of a delay-dependent type moving horizon state-feedback control (MHHC) is considered for a class of linear discrete-time system subject to time-varying state delays, norm-bounded uncertainties, and disturbances with bounded energies. The closed-loop robust stability and robust performance problems are considered to overcome the instability and poor disturbance rejection performance due to the existence of parametric uncertainties and time-delay appeared in the system dynamics. Utilizing a discrete-time Lyapunov-Krasovskii functional, some delay-dependent linear matrix inequality (LMI) based conditions are provided. It is shown that if one can find a feasible solution set for these LMI conditions iteratively at each step of run-time, then we can construct a control law which guarantees the closed-loop asymptotic stability, maximum disturbance rejection performance, and closed-loop dissipativity in view of the actuator limitations. Two numerical examples with simulations on a nominal and uncertain discrete-time, time-delayed systems, are presented at the end, in order to demonstrate the efficiency of the proposed method

H∞ control for networked systems with random communication delays

Copyright [2006] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This note is concerned with a new controller design problem for networked systems with random communication delays. Two kinds of random delays are simultaneously considered: i) from the controller to the plant, and ii) from the sensor to the controller, via a limited bandwidth communication channel. The random delays are modeled as a linear function of the stochastic variable satisfying Bernoulli random binary distribution. The observer-based controller is designed to exponentially stabilize the networked system in the sense of mean square, and also achieve the prescribed H∞ disturbance attenuation level. The addressed controller design problem is transformed to an auxiliary convex optimization problem, which can be solved by a linear matrix inequality (LMI) approach. An illustrative example is provided to show the applicability of the proposed method

Robust Η∞Control for a Class of Discrete Time-Delay Stochastic Systems with Randomly Occurring Nonlinearities

Copyright © 2014 Yamin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In this paper, we consider the robust Η∞ control problem for a class of discrete time-delay stochastic systems with randomly occurring nonlinearities. The parameter uncertainties enter all the system matrices; the stochastic disturbances are both state and control dependent, and the randomly occurring nonlinearities obey the sector boundedness conditions. The purpose of the problem addressed is to design a state feedback controller such that, for all admissible uncertainties, nonlinearities, and time delays, the closed-loop system is robustly asymptotically stable in the mean square, and a prescribed Η∞ disturbance rejection attenuation level is also guaranteed. By using the Lyapunov stability theory and stochastic analysis tools, a linear matrix inequality (LMI) approach is developed to derive sufficient conditions ensuring the existence of the desired controllers, where the conditions are dependent on the lower and upper bounds of the time-varying delays. The explicit parameterization of the desired controller gains is also given. Finally, a numerical example is exploited to show the usefulness of the results obtained.This work was supported in part by the National Natural Science Foundation of China under Grants 61374010, 61074129, and 61175111, the Natural Science Foundation of Jiangsu Province of China under Grant BK2012682, the Qing Lan Project of Jiangsu Province (2010), the 333 Project of Jiangsu Province (2011), and the Six Talents Peak Project of Jiangsu Province (2012)