Observers Design for a Class of Lipschitz Discrete-Time Systems with Time-Delay

The observer design problem for nonlinear time-delay systems becomes more and more a subject of research in constant evolution Germani et al. (2002), Germani & Pepe (2004), Aggoune et al. (1999), Raff & Allgöwer (2006), Trinh et al. (2004), Xu et al. (2004), Zemouche et al. (2006), Zemouche et al. (2007). Indeed, time-delay is frequently encountered in various practical systems, such as chemical engineering systems, neural networks and population dynamic model. One of the recent application of time-delay is the synchronization and information recovery in chaotic communication systems Cherrier et al. (2005). In fact, the time-delay is added in a suitable way to the chaotic system in the goal to increase the complexity of the chaotic behavior and then to enhance the security of communication systems. On the other hand, contrary to nonlinear continuous-time systems, little attention has been paid toward discrete-time nonlinear systems with time-delay. We refer the readers to the few existing references Lu & Ho (2004a) and Lu & Ho (2004b), where the authors investigated the problem of robust H∞ observer design for a class of Lipschitz time-delay systems with uncertain parameters in the discrete-time case. Their method show the stability of the state of the system and the estimation error simultaneously. This chapter deals with observer design for a class of Lipschitz nonlinear discrete-time systems with time-delay. The main result lies in the use of a new structure of the proposed observer inspired from Fan & Arcak (2003). Using a Lyapunov-Krasovskii functional, a new nonrestrictive synthesis condition is obtained. This condition, expressed in term of LMI, contains more degree of freedom than those proposed by the approaches available in literature. Indeed, these last use a simple Luenberger observer which can be derived from the general form of the observer proposed in this paper by neglecting some observer gains. An extension of the presented result to H∞ performance analysis is given in the goal to take into account the noise which affects the considered system. A more general LMI is established. The last section is devoted to systems with differentiable nonlinearities. In this case, based on the use of the Differential Mean Value Theorem (DMVT), less restrictive synthesis conditions are proposed

Robust Predictive Extended State Observer for a Class of Nonlinear Systems with Time-Varying Input Delay

[EN] This paper deals with asymptotic stabilisation of a class of nonlinear input-delayed systems via dynamic output feedback in the presence of disturbances. The proposed strategy has the structure of an observer-based control law, in which the observer estimates and predicts both the plant state and the external disturbance. A nominal delay value is assumed to be known and stability conditions in terms of linear matrix inequalities are derived for fast-varying delay uncertainties. Asymptotic stability is achieved if the disturbance or the time delay is constant. The controller design problem is also addressed and a numerical example with an unstable system is provided to illustrate the usefulness of the proposed strategy.This work was partially supported by: Ministerio de Economía y Competitividad, Spain (TIN2017-86520-C3-1-R); Universitat Politècnica de València (FPI-UPV 2014 PhD Grant); and Israel Science Foundation (Grant No. 1128/14).Sanz Diaz, R.; García Gil, PJ.; Fridman, E.; Albertos Pérez, P. (2020). Robust Predictive Extended State Observer for a Class of Nonlinear Systems with Time-Varying Input Delay. International Journal of Control. 93(2):217-225. https://doi.org/10.1080/00207179.2018.1562204S217225932Ahmed-Ali, T., Cherrier, E., & Lamnabhi-Lagarrigue, F. (2012). Cascade High Gain Predictors for a Class of Nonlinear Systems. IEEE Transactions on Automatic Control, 57(1), 221-226. doi:10.1109/tac.2011.2161795Artstein, Z. (1982). Linear systems with delayed controls: A reduction. IEEE Transactions on Automatic Control, 27(4), 869-879. doi:10.1109/tac.1982.1103023Basturk, H. I. (2017). Cancellation of unmatched biased sinusoidal disturbances for unknown LTI systems in the presence of state delay. Automatica, 76, 169-176. doi:10.1016/j.automatica.2016.10.006Basturk, H. I., & Krstic, M. (2015). Adaptive sinusoidal disturbance cancellation for unknown LTI systems despite input delay. Automatica, 58, 131-138. doi:10.1016/j.automatica.2015.05.013Bekiaris-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:10.1115/1.4005278Besançon, G., Georges, D. & Benayache, Z. (2007). Asymptotic state prediction for continuous-time systems with delayed input and application to control. 2007 European control conference (ECC) (pp. 1786–1791).Engelborghs, K., Dambrine, M., & Roose, D. (2001). Limitations of a class of stabilization methods for delay systems. IEEE Transactions on Automatic Control, 46(2), 336-339. doi:10.1109/9.905705Fridman, E. (2001). New Lyapunov–Krasovskii functionals for stability of linear retarded and neutral type systems. Systems & Control Letters, 43(4), 309-319. doi:10.1016/s0167-6911(01)00114-1Fridman, E. (2014). Introduction to Time-Delay Systems. Systems & Control: Foundations & Applications. doi:10.1007/978-3-319-09393-2Fridman, E. (2014). Tutorial on Lyapunov-based methods for time-delay systems. European Journal of Control, 20(6), 271-283. doi:10.1016/j.ejcon.2014.10.001Furtat, I., Fridman, E., & Fradkov, A. (2018). Disturbance Compensation With Finite Spectrum Assignment for Plants With Input Delay. IEEE Transactions on Automatic Control, 63(1), 298-305. doi:10.1109/tac.2017.2732279Germani, A., Manes, C., & Pepe, P. (2002). A new approach to state observation of nonlinear systems with delayed output. IEEE Transactions on Automatic Control, 47(1), 96-101. doi:10.1109/9.981726Guo, 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.978Karafyllis, I., & Krstic, M. (2017). Predictor Feedback for Delay Systems: Implementations and Approximations. Systems & Control: Foundations & Applications. doi:10.1007/978-3-319-42378-4Krstic, 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.2014.11.003Léchappé, V., Moulay, E. & Plestan, F. (2016). Dynamic observation-prediction for LTI systems with a time-varying delay in the input. 2016 IEEE 55th conference on decision and control (CDC) (pp. 2302–2307).Manitius, 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.1979.1102124Mazenc, F. & Malisoff, M. (2016). New prediction approach for stabilizing time-varying systems under time-varying input delay. 2016 IEEE 55th conference on decision and control (CDC) (pp. 3178–3182).Mondie, S., & Michiels, W. (2003). Finite spectrum assignment of unstable time-delay systems with a safe implementation. IEEE Transactions on Automatic Control, 48(12), 2207-2212. doi:10.1109/tac.2003.820147Najafi, M., Hosseinnia, S., Sheikholeslam, F., & Karimadini, M. (2013). Closed-loop control of dead time systems via sequential sub-predictors. International Journal of Control, 86(4), 599-609. doi:10.1080/00207179.2012.751627Najafi, M., Sheikholeslam, F., Hosseinnia, S., & Wang, Q.-G. (2014). Robust H ∞ control of single input-delay systems based on sequential sub-predictors. IET Control Theory & Applications, 8(13), 1175-1184. doi:10.1049/iet-cta.2012.1004Sanz, R., Garcia, P., & Albertos, P. (2016). Enhanced disturbance rejection for a predictor-based control of LTI systems with input delay. Automatica, 72, 205-208. doi:10.1016/j.automatica.2016.05.019Sanz, R., García, P., & Albertos, P. (2018). A generalized smith predictor for unstable time-delay SISO systems. ISA Transactions, 72, 197-204. doi:10.1016/j.isatra.2017.09.020Sanz, R., García, P., Fridman, E. & Albertos, P. (2017). A predictive extended state observer for a class of nonlinear systems with input delay subject to external disturbances. 2017 IEEE 56th annual conference on decision and control (CDC) (pp. 4345–4350).Sanz, R., Garcia, P., Fridman, E., & Albertos, P. (2018). Rejection of mismatched disturbances for systems with input delay via a predictive extended state observer. International Journal of Robust and Nonlinear Control, 28(6), 2457-2467. doi:10.1002/rnc.4027Shustin, E., & Fridman, E. (2007). On delay-derivative-dependent stability of systems with fast-varying delays. Automatica, 43(9), 1649-1655. doi:10.1016/j.automatica.2007.02.009Suplin, V., Fridman, E., & Shaked, U. (2007). Sampled-data H∞ control and filtering: Nonuniform uncertain sampling. Automatica, 43(6), 1072-1083. doi:10.1016/j.automatica.2006.11.024Yao, J., Jiao, Z., & Ma, D. (2014). RISE-Based Precision Motion Control of DC Motors With Continuous Friction Compensation. IEEE Transactions on Industrial Electronics, 61(12), 7067-7075. doi:10.1109/tie.2014.2321344Zhong, Q.-C. (2004). On Distributed Delay in Linear Control Laws—Part I: Discrete-Delay Implementations. IEEE Transactions on Automatic Control, 49(11), 2074-2080. doi:10.1109/tac.2004.83753

Rejection of mismatched disturbances for systems with input delay via a predictive extended state observer

[EN] The problem of output stabilization and disturbance rejection for input-delayed systems is tackled in this work. First, a suitable transformation is introduced to translate mismatched disturbances into an equivalent input disturbance. Then, an extended state observer is combined with a predictive observer structure to obtain a future estimation of both the state and the disturbance. A disturbance model is assumed to be known but attenuation of unmodeled components is also considered. The stabilization is proved via Lyapunov-Krasovskii functionals, leading to sufficient conditions in terms of linear matrix inequalities for the closed-loop analysis and parameter tuning. The proposed strategy is illustrated through a numerical example.PROMETEOII/2013/004; Conselleria d'Educacio; Generalitat Valenciana, Grant/Award Number: TIN2014-56158-C4-4-P-AR; Ministerio de Economia y Competitividad, Grant/Award Number: FPI-UPV 2014; Universitat Politecnica de ValenciaSanz Diaz, R.; García Gil, PJ.; Fridman, E.; Albertos Pérez, P. (2018). Rejection of mismatched disturbances for systems with input delay via a predictive extended state observer. International Journal of Robust and Nonlinear Control. 28(6):2457-2467. https://doi.org/10.1002/rnc.4027S24572467286Stability and Stabilization of Systems with Time Delay. (2011). IEEE Control Systems, 31(1), 38-65. doi:10.1109/mcs.2010.939135Fridman, E. (2014). Introduction to Time-Delay Systems. Systems & Control: Foundations & Applications. doi:10.1007/978-3-319-09393-2Watanabe, K., & Ito, M. (1981). A process-model control for linear systems with delay. IEEE Transactions on Automatic Control, 26(6), 1261-1269. doi:10.1109/tac.1981.1102802Astrom, K. J., Hang, C. C., & Lim, B. C. (1994). A new Smith predictor for controlling a process with an integrator and long dead-time. IEEE Transactions on Automatic Control, 39(2), 343-345. doi:10.1109/9.272329Matausek, M. R., & Micic, A. D. (1996). A modified Smith predictor for controlling a process with an integrator and long dead-time. IEEE Transactions on Automatic Control, 41(8), 1199-1203. doi:10.1109/9.533684García, P., & Albertos, P. (2008). A new dead-time compensator to control stable and integrating processes with long dead-time. Automatica, 44(4), 1062-1071. doi:10.1016/j.automatica.2007.08.022Normey-Rico, J. E., & Camacho, E. F. (2009). Unified approach for robust dead-time compensator design. Journal of Process Control, 19(1), 38-47. doi:10.1016/j.jprocont.2008.02.003Manitius, 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.1982.1103023Krstic, 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.2014.11.003Sanz, R., Garcia, P., & Albertos, P. (2016). Enhanced disturbance rejection for a predictor-based control of LTI systems with input delay. Automatica, 72, 205-208. doi:10.1016/j.automatica.2016.05.019Basturk, H. I., & Krstic, M. (2015). Adaptive sinusoidal disturbance cancellation for unknown LTI systems despite input delay. Automatica, 58, 131-138. doi:10.1016/j.automatica.2015.05.013Basturk, H. I. (2017). Cancellation of unmatched biased sinusoidal disturbances for unknown LTI systems in the presence of state delay. Automatica, 76, 169-176. doi:10.1016/j.automatica.2016.10.006Sanz, R., Garcia, P., Albertos, P., & Zhong, Q.-C. (2016). 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. doi:10.1002/rnc.3639Mondie, S., & Michiels, W. (2003). Finite spectrum assignment of unstable time-delay systems with a safe implementation. IEEE Transactions on Automatic Control, 48(12), 2207-2212. doi:10.1109/tac.2003.820147Zhong, Q.-C. (2004). On Distributed Delay in Linear Control Laws—Part I: Discrete-Delay Implementations. IEEE Transactions on Automatic Control, 49(11), 2074-2080. doi:10.1109/tac.2004.837531Zhou, B., Lin, Z., & Duan, G.-R. (2012). Truncated predictor feedback for linear systems with long time-varying input delays. Automatica, 48(10), 2387-2399. doi:10.1016/j.automatica.2012.06.032Zhou, B., Li, Z.-Y., & Lin, Z. (2013). On higher-order truncated predictor feedback for linear systems with input delay. International Journal of Robust and Nonlinear Control, 24(17), 2609-2627. doi:10.1002/rnc.3012Besançon G Georges D Benayache Z Asymptotic state prediction for continuous-time systems with delayed input and application to control IEEE 2007 Kos, GreeceNajafi, M., Hosseinnia, S., Sheikholeslam, F., & Karimadini, M. (2013). Closed-loop control of dead time systems via sequential sub-predictors. International Journal of Control, 86(4), 599-609. doi:10.1080/00207179.2012.751627Léchappé V Moulay E Plestan F Dynamic observation-prediction for LTI systems with a time-varying delay in the input IEEE 2016 Las Vegas, NVCacace, 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.3517Mazenc, F., & Malisoff, M. (2017). Stabilization of Nonlinear Time-Varying Systems Through a New Prediction Based Approach. IEEE Transactions on Automatic Control, 62(6), 2908-2915. doi:10.1109/tac.2016.2600500Guo, 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.978Fridman, E. (2003). Output regulation of nonlinear systems with delay. Systems & Control Letters, 50(2), 81-93. doi:10.1016/s0167-6911(03)00131-2Isidori, A., & Byrnes, C. I. (1990). Output regulation of nonlinear systems. IEEE Transactions on Automatic Control, 35(2), 131-140. doi:10.1109/9.45168Ding, Z. (2003). Global stabilization and disturbance suppression of a class of nonlinear systems with uncertain internal model. Automatica, 39(3), 471-479. doi:10.1016/s0005-1098(02)00251-0Chen, 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.2015.2478397Fridman, 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., & Orlov, Y. (2009). Exponential stability of linear distributed parameter systems with time-varying delays. Automatica, 45(1), 194-201. doi:10.1016/j.automatica.2008.06.00

Robust ∞ Filtering for a Class of Complex Networks with Stochastic Packet Dropouts and Time Delays

The robust ∞ filtering problem is investigated for a class of complex network systems which has stochastic packet dropouts and time delays, combined with disturbance inputs. The packet dropout phenomenon occurs in a random way and the occurrence probability for each measurement output node is governed by an individual random variable. Besides, the time delay phenomenon is assumed to occur in a nonlinear vector-valued function. We aim to design a filter such that the estimation error converges to zero exponentially in the mean square, while the disturbance rejection attenuation is constrained to a given level by means of the ∞ performance index. By constructing the proper Lyapunov-Krasovskii functional, we acquire sufficient conditions to guarantee the stability of the state detection observer for the discrete systems, and the observer gain is also derived by solving linear matrix inequalities. Finally, an illustrative example is provided to show the usefulness and effectiveness of the proposed design method

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

Mathematical control of complex systems

Copyright © 2013 ZidongWang 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

H ∞ sliding mode observer design for a class of nonlinear discrete time-delay systems: A delay-fractioning approach

Copyright @ 2012 John Wiley & SonsIn this paper, the H ∞  sliding mode observer (SMO) design problem is investigated for a class of nonlinear discrete time-delay systems. The nonlinear descriptions quantify the maximum possible derivations from a linear model, and the system states are allowed to be immeasurable. Attention is focused on the design of a discrete-time SMO such that the asymptotic stability as well as the H ∞  performance requirement of the error dynamics can be guaranteed in the presence of nonlinearities, time delay and external disturbances. Firstly, a discrete-time discontinuous switched term is proposed to make sure that the reaching condition holds. Then, by constructing a new Lyapunov–Krasovskii functional based on the idea of ‘delay fractioning’ and by introducing some appropriate free-weighting matrices, a sufficient condition is established to guarantee the desired performance of the error dynamics in the specified sliding mode surface by solving a minimization problem. Finally, an illustrative example is given to show the effectiveness of the designed SMO design scheme

Recent advances on recursive filtering and sliding mode design for networked nonlinear stochastic systems: A survey

Copyright © 2013 Jun Hu 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.Some recent advances on the recursive filtering and sliding mode design problems for nonlinear stochastic systems with network-induced phenomena are surveyed. The network-induced phenomena under consideration mainly include missing measurements, fading measurements, signal quantization, probabilistic sensor delays, sensor saturations, randomly occurring nonlinearities, and randomly occurring uncertainties. With respect to these network-induced phenomena, the developments on filtering and sliding mode design problems are systematically reviewed. In particular, concerning the network-induced phenomena, some recent results on the recursive filtering for time-varying nonlinear stochastic systems and sliding mode design for time-invariant nonlinear stochastic systems are given, respectively. Finally, conclusions are proposed and some potential future research works are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61329301, 61333012, 61374127 and 11301118, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant no. GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

New advances in H∞ control and filtering for nonlinear systems

The main objective of this special issue is to summarise recent advances in H∞ control and filtering for nonlinear systems, including time-delay, hybrid and stochastic systems. The published papers provide new ideas and approaches, clearly indicating the advances made in problem statements, methodologies or applications with respect to the existing results. The special issue also includes papers focusing on advanced and non-traditional methods and presenting considerable novelties in theoretical background or experimental setup. Some papers present applications to newly emerging fields, such as network-based control and estimation