H2 Robust Filter Design With Performance Certificate Via Convex Programming

In this paper a new approach to H2 robust filter design is proposed. Both continuous- and discrete-time invariant systems subject to polytopic parameter uncertainty are considered. After a brief discussion on some of the most expressive methods available for H2 robust filter design, a new one based on a performance certificate calculation is presented. The performance certificate is given in terms of the gap produced by the robust filter between lower and upper bounds of a minimax programming problem where the H2 norm of the estimation error is maximized with respect to the feasible uncertainties and minimized with respect to all linear, rational and causal filters. The calculations are performed through convex programming methods developed to deal with linear matrix inequality (LMI). Many examples borrowed from the literature to date are solved and it is shown that the proposed method outperforms all other designs. © 2007 Elsevier Ltd. All rights reserved.444937948Anderson, B.D.O., Moore, J.B., (1979) Optimal filtering, , Prentice Hall, Englewood Cliffs, NJBarbosa, K.A., de Souza, C.E., Trofino, A., Robust H2 filtering for uncertain linear systems: LMI based methods with parametric Lyapunov functions (2005) Systems & Control Letters, 54 (3), pp. 251-262Boyd, S.P., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear matrix inequalities in system and control theory, , SIAM, PhiladelphiaColaneri, J., Geromel, C., Locatelli, A., (1997) Control theory and design-An RH2 and RH∞ viewpoint, , Academic Press, New YorkGeromel, J.C., Convex analysis and global optimization of joint actuator location and control problems (1989) IEEE Transactions on Automatic Control, 34 (7), pp. 711-720Geromel, J.C., Optimal linear filtering under parameter uncertainty (1999) IEEE Transactions on Signal Processing, 47 (1), pp. 168-175Geromel, J.C., de Oliveira, M.C., Bernussou, J., Robust filtering of discrete-time linear systems with parameter dependent Lyapunov functions (2002) SIAM Journal on Control Optimization, 41 (3), pp. 700-711Geromel, J.C., de Oliveira, M.C., Hsu, L., LMI characterization of structural and robust stability (1998) Linear Algebra and Its Applications, 285, pp. 69-80Geromel, J.C., Regis, L.A.V., H2 Optimal robust filtering (2006) European Journal of Control, 12 (1), pp. 30-39Hoang, N.T., Tuan, H.D., Apkarian, P., Hosoe, S., Robust filtering for discrete nonlinear fractional transformation systems (2004) IEEE Transactions Circuit and Systems II-Express Briefs, 51, pp. 587-592Jain, B.N., Guaranteed error estimation in uncertain systems (1975) IEEE Transactions on Automatic Control, 20, pp. 230-232Li, L., Luo, Z.Q., Davidson, T.N., Wong, K.M., Bossé, E., Robust filtering via semidefinite programming with applications to target tracking (2002) SIAM Journal on Optimization, 12 (3), pp. 740-755Martin, C.J., Mintz, M., Robust filtering and prediction for linear systems with uncertain dynamics: A game-theoretic approach (1983) IEEE Transactions on Automatic Control, 28 (9), pp. 888-896Meirovitch, L., Baruh, H., Oz, H., A comparison of control techniques for large flexible systems (1983) J. Guidance, 6 (4), pp. 302-310de Oliveira, M.C., Geromel, J.C., Hsu, L., LMI characterization of structural and robust stability: The discrete-time case (1999) Linear Algebra and Its Applications, 296, pp. 27-38Poor, H.V., On robust wiener filtering (1980) IEEE Transactions on Automatic Control, 25 (3), pp. 531-536Rockafellar, R., (1970) Convex analysis, , Princeton PressScherer, C. W., Köse, I. E. (2006). Robust H2 estimation with dynamic IQCs: A convex solution. In IEEE Conference on Decision and Control, USAShaked, U., Xie, L., Soh, Y.C., New approaches to robust minimum variance filter design (2001) IEEE Transactions on Signal Processing, 49 (11), pp. 2620-2629de Souza, C.E., Trofino, A., An LMI approach to the design of robust H2 filters (1999) Recent Advances on linear matrix inequalities methods in control, , El Ghaoui L., and Niculescu S.-I. (Eds), SIAM, Englewood Cliffs, NJTheodor, Y., Shaked, U., Robust discrete-time minimum variance filtering (1996) IEEE Transactions on Signal Processing, 44, pp. 181-189Tuan, H.D., Apkarian, P., Nguyen, T.Q., Robust and reduce-order filtering : New LMI-based characterizations and methods (2001) IEEE Transactions on Signal Processing, 49 (12), pp. 2975-2984Xie, L.H., Soh, Y.C., Robust Kalman filtering for uncertain systems (1994) Systems Control Letters, 22, pp. 123-129Xie, L.H., Soh, Y.C., de Souza, C.E., Robust Kalman filtering for uncertain discrete-time systems (1994) IEEE Transactions on Automatic Control, 39, pp. 1310-1314Xie, L. H., Soh, Y. C., Du, C. (1999). RobustH2 estimation and control. School of Electrical and Electronic Engineering Nanyang Technological University, Singapore, Technical Repor

Matrix Quadratic Polynomials With Application To Robust Stability Analysis

This paper provides robust stability conditions for continuous and discrete time polytopic systems. They are obtained from linear and fractional parameter dependent Lyapunov functions and are expressed in terms of linear matrix inequalities-LMI. As an immediate generalization, a tight upper bound of the associated guaranteed H2 cost is determined. Numerical examples are included for illustration and comparison purpose with other robust stability conditions for continuous and discrete time systems available in the literature to date. Copyright © 2005 IFAC.5PART 1549554Apkarian, P., Tuan, H.D., Parameterized LMIs in control theory (2000) SIAM on Control Optim., 38 (4), pp. 1241-1264Bliman, P.A., A convex approach to robust stability for linear systems with uncertain scalar parameters (2004) SIAM on Control Optim., 42 (46), pp. 2016-2042Boyd, S.P., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory, , SIAM, Philadelphia, 1994Chesi, G., Garulli, A., Tesi, A., Vicino, A., Polynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems : An LMI approach (2005) IEEE Trans. Automat. Contr., 50 (3), pp. 365-379Dettori, M., Scherer, C.W., New robust stability and performance conditions based on parameter dependent multipliers (2000) Proccedings of IEEE CDC, , Sydney, AustraliaGahinet, P., Apkarian, P., Chilali, M., Affine parameter-dependent Lyapunov functions and real parametric uncertainty (1996) IEEE Transactions on Automatic Control, 41 (3), pp. 436-442. , PII S0018928696021216Geromel, J.C., Peres, P.L.D., Bernussou, J., On a convex parameter space method for linear control design of uncertain systems (1991) SIAM Journal on Control and Optim., 29 (2), pp. 381-402Geromel, J.C., De Oliveira, M.C., Hsu, L., LMI characterization of structural and robust stability (1998) Linear Algebra Appl., 285, pp. 69-80Luenberger, D.G., (1979) Introduction to Dynamic Systems : Theory, Models and Applications, 1979. , John Wiley $ Sons, New YorkDe Oliveira, M.C., Geromel, J.C., Hsu, L., LMI characterization of structural and robust stability: The discrete-time case (1999) Linear Algebra and Its Applications, 296 (1-3), pp. 27-38. , PII S0024379599000865De Oliveira, M.C., Bernussou, J., Geromel, J.C., A new discrete-time robust stability condition (1999) Systems and Control Letters, 37 (4), pp. 261-265. , PII S0167691199000353Ramos, D.C.W., Peres, P.L.D., A less conservative LMI condition for the robust stability of discrete-time uncertain systems (2001) Systems and Control Letters, 43 (5), pp. 371-378. , DOI 10.1016/S0167-6911(01)00120-7, PII S0167691101001207Ramos, D.C.W., Peres, P.L.D., An LMI condition for the robust stability of uncertain continuous-time linear systems (2002) IEEE Transactions on Automatic Control, 47 (4), pp. 675-678. , DOI 10.1109/9.995048, PII S0018928602037509Trofino, A., De Souza, C.E., Biquadratic stability of uncertain linear systems (2001) IEEE Transactions on Automatic Control, 46 (8), pp. 1303-1307. , DOI 10.1109/9.940939, PII S001892860107693

H∞ Control Design For Time-delay Linear Systems: A Rational Transfer Function Based Approach

The aim of this paper is to present new results on H∞ control synthesis for time-delay linear systems. We extend the use of a finite order LTI system, called comparison system to H∞ analysis and design. Differently from what can be viewed as a common feature of other control design methods available in the literature to date, the one presented here treats time-delay systems control design with classical numeric routines based on Riccati equations arisen from H∞ theory. The proposed algorithm is simple, efficient and easy to implement. Some examples illustrating state and output feedback design are solved and discussed in order to put in evidence the most relevant characteristic of the theoretical results. Moreover, a practical application involving a 3-DOF networked control system is presented. © 2012 EUCA.185425436Boukas, E.-K., Liu, Z.-K., (2002) Deterministic and Stochastic Time Delay Systems, Control Engineering, , Birkhäuser, BostonByrd, R.H., Schnabel, R.B., Continuity of the null space basis and constrained optimization (1986) Math Program, 35 (1), pp. 32-41Choi, H.H., Chungs, M.J., Observer-based H∞ controller design for state delayed linear systems (1995) Automatica, 32 (7), pp. 1073-1075Colaneri, P., Geromel, J.C., Locatelli, A., (1997) Control Theory and Design: An RH2-RH∞ Viewpoint, , Academic Press Inc., London, UKde Oliveira, M.C., Geromel, J.C., Synthesis of non-rational controllers for linear delay systems (2004) Automatica, 40 (2), pp. 171-188de Oliveira, M.C., Souza, F.O., Palhares, R.M., Assessing Stability of Time-Delay Systems Using Rational Systems (2008) Proceedings of the 47th IEEE Conference on Decision and Control, pp. 4012-4017. , Cancun, Mexico, December 9-11Fridman, E., Shaked, U., New bounded real lemma representations for time-delay systems and their applications (2001) IEEE Trans Autom Control, 46 (12), pp. 1973-1979Fridman, E., Shaked, U., A descriptor system approach to H∞ control of linear time-delay systems (2002) IEEE Trans Autom Control, 47 (2), pp. 253-270Ge, J.-H., Frank, P.M., Lin, C.-F., H∞ control via output feedback for state delayed systems (1996) Int J Control, 64 (1), pp. 1-7Gu, K., Kharitonov, V.L., Chen, J., (2003) Stability of Time-Delay Systems, Control Engineering, , Birkhäuser, BostonHespanha, J.P., Naghshtabrizi, P., Xu, Y., A survey of recent results in networked control systems (2007) Proc IEEE, 95 (1), pp. 138-162Korogui, R.H., Fioravanti, A.R., Geromel, J.C., On a rational transfer function-based approach to H∞ filter design for time-delay linear systems (2011) IEEE Trans Signal Process, 59 (3), pp. 979-988Lee, J.H., Kim, W., Kwon, W.H., Memoryless H∞ controllers for state delayed systems (1994) IEEE Trans Autom Control, 39 (1), pp. 159-162Niculescu, S.I., H∞ memoryless control with an α-stability constraint for time-delay systems: An LMI approach (1998) IEEE Trans Autom Control, 43 (5), pp. 739-748Niculescu, S.I., Gu, K., (2004) Advances in Time-Delay Systems, , SpringerOlgac, N., Sipahi, R., An exact method for the stability analysis of time-delayed linear time-invariant (LTI) systems (2002) IEEE Trans Autom Control, 47 (5), pp. 793-797(2010) 3 DOF Hover System, , www.quanser.com, QuanserRekasius, Z.V., A Stability Test for Systems with Delays (1980) Proc. of Joint Automatic Control Conference, , Paper No. TP9-ARichard, J.-P., Time delay systems: Anoverviewof some recent advances and open problems (2003) Automatica, 39 (10), pp. 1667-1694Roesch, O., Roth, H., Niculescu, S.-I., Remote Control of Mechatronic Systems Over Communication Networks (2005) Proc. IEEE Inter. Conf. Mechatronics & Automation, pp. 1648-1653. , Niagara Falls, Canada, JulyShen, J.-C., Chen, B.-S., Kung, F.-C., Memoryless stabilization of uncertain dynamic delay systems: Riccati equation approach (1991) IEEE Trans Autom Control, 36 (5), pp. 638-640Sipahi, R., Olgac, N., A Comparison of Methods Solving the Imaginary Characteristic Roots of LTI Time Delayed Systems (2005) Proceedings of the IFAC World Congress, , Prague, Czech RepublicZhang, J., Knospe, C.R., Tsiotras, P., New results for the analysis of linear systems with time-invariant delays (2003) Int J Robust Nonlinear Control, 13 (12), pp. 1149-1175Zhang, L., Shi, Y., Chen, T., Huang, B., A new method for stabilization of networked control systems with random delays (2005) IEEE Trans Autom Control, 50 (8), pp. 1177-1181Zhang, W., Branicky, M.S., Phillips, S.M., Stability of networked control systems (2001) IEEE Control Syst Mag, pp. 84-99Zhou, K., Doyle, J.C., (1998) Essentials of Robust Control, , Prentice Hall, New Jerse

Robust H2 Filtering For Discrete Lti Systems With Linear Fractional Representation

This paper introduces a new approach to H2 robust filtering design for discrete LTI systems subjected to linear fractional parameter uncertainty representation. We calculate a performance certificate in terms of the gap between the lower and the upper bounds of a minimax programming problem, which defines the optimal robust filter and the associated equilibrium cost. The calculations are performed through convex programming methods, applying slack variables, known as multipliers, to handle the fractional dependence of the plant transfer function with respect to the parameter uncertainty. The theory is illustrated by means of an example borrowed from the literature and a practical application involving the design of a robust filter for the load voltage estimation on a transmission line with a stub feeding an unknown resistive load. © 2008 IEEE.19021907Anderson, B.D.O., Moore, J.B., (1979) Optimal Filtering, , Englewood Cliffs, New JerseyBoyd, S.P., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory, , SIAM, PhiladelphiaGeromel, J.C., de Oliveira, M.C., Bernussou, J., Robust filtering of discrete-time linear systems with parameter dependent Lyapunov functions (2002) SIAM J. Optim. Contr, 41 (3), pp. 700-711Geromel, J.C., Korogui, R.H., H2 robust filter design with performance certificate via convex programming (2008) Automatica, 44 (4), pp. 937-948Geromel, J.C., Regis Filho, L.A.V., H2 optimal robust filtering (2006) European Journal of Control, 12 (1), pp. 30-39Hoang, N.T., Tuan, H.D., Apkarian, P., Hosoe, S., Robust filtering for discrete nonlinear fractional transformation systems (2004) IEEE Trans. Circ. Syst.-II, 51 (11), pp. 587-592. , NovemberIwasaki, T., Hara, S., Well-posedness of feedback systems: Insights into exact robustness analysis and approximate computations (1998) IEEE Trans. on Automat. Contr, 43 (5), pp. 619-630. , MayKorogui, R.H., Geromel, J.C., Robust H2 Filtering for Continuous Time Systems with Linear Fractional Representation (2008) Proceedings of the 17th IFAC World Congress, pp. 2675-2680. , Seoul, Korea, JulyMatick, R.E., (1969) Transmission Lines for Digital and Communication Networks, , McGraw-HillRockafellar, R., (1970) Convex Analysis, , Princeton PressScherer, C.W., Köse, I.E., Robust H2 estimation with dynamic IQCs: A convex solution (2006) Proceedings of the 45th IEEE CDC, pp. 4746-4751. , San Diego, CA, DecemberShaked, U., Xie, L., Soh, Y.C., New approachs to robust minimum variance filter design (2001) IEEE Trans. Signal Proces, 49 (11). , 2620-2629, NovemberTheodor, Y., Shaked, U., Robust discrete-time minimum variance filtering (1996) IEEE Trans. Signal Proces, 44, pp. 181-18

On A Rational Transfer Function-based Approach To ℋ∞ Filter Design For Time-delay Linear Systems

This paper considers the problem of ℋ∞ filter design for time-delay systems. An LTI finite dimensional system, called comparison system, is constructed in order to exploit recent results on stability analysis and ℋ∞ norm calculation, which were proven to be strongly related to those of time-delay systems. Differently of what can be viewed as a common feature of filter design methods available in the literature to date, the one presented here addresses time-delay systems filtering with classical numeric routines based on Riccati equation and ℋ∞ theory of LTI systems. The design algorithm is simple, efficient and easy to implement. An illustrative example is solved and is used to put in evidence the most important characteristic of the design procedure. ©2009 IEEE.18541859Brockett, R., Byrnes, C., Multivariable Nyquist Criteria, Root Loci, and Pole Placement: A Geometric Viewpoint (1981) IEEE Transac. on Automatic Control, 26, pp. 271-284Chen, J., Gu, G., Nett, C.N., A New Method for Computing Delay Margins for Stability of Linear Delay Systems (1995) Systems & Control Letters, 26 (2), pp. 107-117Chiasson, J., A Method for Computing the Interval of Delay Values for which a Differential-Delay System is Stable (1988) IEEE Transac. on Automatic Control, 33 (12), pp. 1176-1178Colaneri, P., Geromel, J.C., Locatelli, A., (1997) Control Theory and Design: An RH2 -RH∞ Viewpoint, , Academic Press Inc., London, UKDe Oliveira, M.C., Geromel, J.C., Synthesis of Nonrational Controllers for Linear Delay Systems (2004) Automatica, 40 (2), pp. 171-188Fridman, E., Shaked, U., A New H∞ Filter Design for Linear Time-Delay Systems (2001) IEEE Trans. Signal Processing, 49 (11), pp. 2839-2843Fridman, E., Shaked, U., Xie, L., Robust H∞ Filtering of Linear Systems with Time-Varying Delay (2003) IEEE Trans. Automatic Control, 48 (1), pp. 159-165Fridman, E., Shaked, U., An Improved Delay-Dependent H∞ Filtering of Linear Neutral Systems (2004) IEEE Trans. Signal Processing, 52 (3), pp. 668-673Geromel, J.C., Korogui, R.H., (2009) Stability Analysis and H∞ Control Design of Time Delay Systems Usign a Rational Comparison System, , SubmittedGu, K., Kharitonov, V.L., Chen, J., (2003) Stability of Time-Delay Systems, , Control Engineering Series, BirkhäuserNiculescu, S.I., Gu, K., (2004) Advances in Time-Delay Systems, , SpringerPila, A.W., Shaked, U., De Souza, C.E., H∞ Filtering for Continuous-Time Linear Systems with Delay (1999) IEEE Transac. on Automatic Control, 44 (7), pp. 1412-1417Rekasius, Z.V., A Stability Test for Systems with Delays (1980) Proc. Joint Automatic Control Conf., , Paper No. TP9-ARichard, J.P., Time-Delay Systems: An Overview of Some Recent Advances and Open Problems (2003) Automatica, 39 (10), pp. 1667-1694Olgac, N., Sipahi, R., An Exact Method for the Stability Analysis of Time-Delayed Linear Time-Invariant (LTI) Systems (2002) IEEE Transac. on Automatic Control, 47 (5), pp. 793-797Walton, K., Marshall, J.E., Direct Method for TDS Stability Analysis (1987) IEE Proceedings, 134 (2), pp. 101-107. , Pt. DYoucef-Toumi, K., Bobbett, J., Stability of Uncertain Linear Systems with Time Delay (1991) Journal of Dynamic Systems, Measurement, and Control, 113 (4), pp. 558-567Zhang, X.M., Han, Q.L., Robust H∞ Filtering for a Class of Uncertain Linear Systems with Time-Varying Delay (2008) Automatica, 44 (1), pp. 157-166Zhang, J., Knospe, C.R., Tsiotras, P., New Results for the Analysis of Linear Systems with Time Invariant Delays (2003) Int. Journal of Robust and Nonlinear Contr., 13 (12), pp. 1149-1175Zhou, K., Doyle, J.C., (1998) Essentials of Robust Control, , Prentice Hall, New Jerse

On Robust Output Feedback Control For Polytopic Systems

Robust dynamic output feedback design is an open problem, computationally speaking, since its determination asks for the solution of nonlinear matrix inequalities, namely bilinear ones. This is particularly the case, for polytopic uncertainty. Here a new sufficient condition is proposed by the use of bounds and scaling for completion of squares. The usefulness of the provided conditions stands in the fact that its solution can be performed using the Frank-Wolfe algorithm which runs in only one shot. The control design of an inverted pendulum with uncertain friction coefficients illustrates the theory. © 2005 IEEE.200550185023Boyd, S.P., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory, , SIAM, PhiladelphiaDoyle, J.C., Stein, G., Multivarible feedback design - Concepts for a classical modern synthesis (1981) IEEE Trans. Automat. Contr, 26 (1), pp. 4-16Doyle, J.C., Glover, K., Khargonekar, P.P., Francis, B.A., State space solutions to standard H2 and H∞, control problems (1989) IEEE Trans. Automat. Contr, 34 (8), pp. 831-847Doyle, J.C., Zhou, K.M., Glover, K., Bodenheimer, B., Mixed H2 and H∞, performance objectives - optimal control (1994) IEEE Trans. Automat. Contr, 39 (8), pp. 1575-1587Gahinet, P., Apkarian, P., A linear matrix inequality approach to H∞ control (1994) Inter Jour of Robust and Nonlinear Contr, 4 (4), pp. 421-448Geromel, J.C., Palhares, A.G.B., Análise Linear de Sistemas Dinâmicos : Teoria, Ensaios Práticos e (2004) Exercícios (in Portuguese), Editora Edgard Blucher LTDA, , São Paulo, BrazilGeromel, J.C., Bernussou, J., de Oliveira, M.C., H-2-norm optimization with constrained dynamic output feedback controllers: Decentralized and reliable control (1999) IEEE Trans. Automat. Contr, 44 (7), pp. 1449-1454Zames, G., Feedback and optimal sensitivity - model reference transformations, multiplicative seminorms and approximate inverses (1981) IEEE Trans. Automat. Contr, 26 (2), pp. 301-320Zames, G., Francis, B.A., Feedback, minimax sensitivity and optimal robustness (1983) IEEE Trans. Automat. Contr, 28 (5), pp. 585-60

H ∞ Control Design For Time-delay Linear Systems: A Rational Transfer Function Based Approach

The aim of this paper is to cope with the H ∞ control synthesis for time-delay linear systems. We extend the use of a finite order LTI system, called comparison system to H ∞ analysis and design. Differently from what can be viewed as a common feature of other control design methods available in the literature to date, the one presented here treats time-delay systems control design with classical numeric routines based on Riccati equation and H ∞ theory. An illustrative example and a practical application involving a 3-DOF networked control system are presented. © 2011 IEEE.18661871Boukas, E.-K., Liu, Z.-K., (2002) Deterministic and Stochastic Time Delay Systems, , Control Engineering. BirkhäuserByrd, R.H., Schnabel, R.B., Continuity of the null space basis and constrained optimization (1986) Mathematical Programming, 35 (1), pp. 32-41Ho Choi, H., Chungs, M.J., Observer-based H ∞ controller design for state delayed linear systems (1995) Automatica, 32 (7), pp. 1073-1075Colaneri, P., Geromel, J.C., Locatelli, A., (1997) Control Theory and Design: An RH 2 - RH ∞ Viewpoint, , Academic Press, LondonDe Oliveira, M.C., Geromel, J.C., Synthesis of non-ratinal controllers for linear delay systems (2004) Automatica, 40 (2), pp. 171-188Fridman, E., Shaked, U., New bounded real lemma representations for time-delay systems and their applications (2001) IEEE Trans. Autom. Contr., 46 (12), pp. 1973-1979Fridman, E., Shaked, U., A descriptor system approach to H ∞ control of linear time-delay systems (2002) IEEE Trans. Autom. Contr., 47 (2), pp. 253-270Ge, J.-H., Frank, P.M., Lin, C.-F., H ∞ control via output feedback for state delayed systems (1996) Int. Jour. Contr., 64 (1), pp. 1-7Gu, K., Kharitonov, V.L., Chen, J., (2003) Stability of Time-delay Systems, , Control Eng. Series. BirkhuserHespanha, J.P., Naghshtabrizi, P., Xu, Y., A survey of recent results in networked control systems (2007) Proceedings of the IEEE, 95 (1), pp. 138-162Korogui, R.H., Fioravanti, A.R., Geromel, J.C., On a rational transfer function-based approach to H ∞ filter design for time-delay linear systems (2011) IEEE Trans. Sign. Process, 59 (3), pp. 979-988Lee, J.H., Kim, W., Kwon, W.H., Memoryless H ∞ controllers for state delayed systems (1994) IEEE Trans. Autom. Contr., 39 (1), pp. 159-162Niculescu, S.I., H ∞ memoryless control with an α-stability constraint for time-delay systems: An lmi approach (1998) IEEE Trans. Autom. Control, 43 (5), pp. 739-748Niculescu, S.I., Gu, K., (2004) Advances in Time-delay Systems, , SpringerOlgac, N., Sipahi, R., An exact method for the stability analysis of time-delayed linear time-invariant (lti) systems (2002) IEEE Trans. Autom. Contr., 47 (5), pp. 793-797(2010) 3 DOF Hover System, , www.quanser.comRekasius, Z.V., A stability test for systems with delays (1980) Proc. of Joint Automatic Control Conference, Paper No. TP9-ARichard, J.-P., Time delay systems: An overview of some recent advances and open problems (2003) Automatica, 39 (10), pp. 1667-1694Roesch, O., Roth, H., Niculescu, S.-I., Remote control of mechatronic systems over communication networks (2005) Proc. IEEE Inter. Conf. Mechatronics & Automation, pp. 1648-1653. , Niagara Falls, Canada, JulyShen, J.-C., Chen, B.-S., Kung, F.-C., Memoryless stabilization of uncertain dynamic delay systems: Riccati equation approach (1991) IEEE Trans. Autom. Contr., 36 (5), pp. 638-640Sipahi, R., Olgac, N., A comparison of methods solving the imaginary characteristic roots of lti time delayed systems (2005) Proceedings of the IFAC World Congress, , Prague, Czech RepublicZhang, J., Knospe, C.R., Tsiotras, P., New results for the analysis of linear systems with time-invariant delays (2003) Int. Journal Rob. Nonlin. Control, 13 (12), pp. 1149-1175Zhang, L., Shi, Y., Chen, T., Huang, B., A new method for stabilization of networked control systems with random delays (2005) IEEE Transactions on Automatic Control, 50 (8), pp. 1177-1181Zhang, W., Branicky, M.S., Phillips, S.M., Stability of networked control systems (2001) IEEE Control Systems Magazine, pp. 84-99Zhou, K., Doyle, J.C., (1998) Essentials of Robust Control, , Prentice Hall, New Jerse

H2 And H∞ Robust Output Feedback Control For Continuous Time Polytopic Systems

Robust dynamic output feedback design is an open problem, computationally speaking, since its determination asks for the solution of nonlinear matrix inequalities, namely bilinear ones. This is particularly the case for polytopic uncertainty. Here, new sufficient conditions for 2 and ∞ robust output feedback control synthesis are proposed by the use of bounds and scaling for completion of squares. The usefulness of the provided conditions stands in the fact that its solution can be performed using the Frank-Wolfe algorithm which runs in only one shot. The 2 robust control design of an inverted pendulum with uncertain friction coefficients and ∞ reliable control systems design illustrate the theory. © The Institution of Engineering and Technology 2007.1515411549Zames, G., Feedback and optimal sensitivity - Model reference transformations, multiplicative seminorms and approximate inverses (1981) IEEE Trans. Autom. Control, 26 (2), pp. 301-320. , 10.1109/TAC.1981.1102603 0018-9286Zames, G., Francis, B.A., Feedback, minimax sensitivity and optimal robustness (1983) IEEE Trans. Autom. Control, 28 (5), pp. 585-601. , 10.1109/TAC.1983.1103275 0018-9286Doyle, J.C., Stein, G., Multivarible feedback design - Concepts for a classical modern synthesis (1981) IEEE Trans. Autom. Control, 26 (1), pp. 4-16. , 10.1109/TAC.1981.1102555 0018-9286Doyle, J.C., Glover, K., Khargonekar, P.P., Francis, B.A., State space solutions to standard 2 and ∞ control problems (1989) IEEE Trans. Autom. Control, 34 (8), pp. 831-847. , 10.1109/9.29425 0018-9286Doyle, J.C., Zhou, K.M., Glover, K., Bodenheimer, B., Mixed 2 and ∞ performance objectives - Optimal control (1994) IEEE Trans. Autom. Control, 39 (8), pp. 1575-1587. , 10.1109/9.310031 0018-9286Boyd, S.P., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory, , SIAM, PhiladelphiaHenrion, D., Lasserre, J.B., Convergent relaxations of polynomial matrix inequalities and static output feedback (2006) IEEE Trans. Autom. Control, 51 (2), pp. 192-202. , 10.1109/TAC.2005.863494 0018-9286Gahinet, P., Apkarian, P., A linear matrix inequality approach to ∞ control (1994) Int. J. Robust Nonlinear Control, 4 (4), pp. 421-448. , 1049-8923Geromel, J.C., Bernussou, J., De Oliveira, M.C., 2 norm optimization with constrained dynamic output feedback controllers: Decentralized and reliable control (1999) IEEE Trans. Automat. Control, 44 (7), pp. 1449-1454. , 10.1109/9.774121 0018-9286El Ghaoui, L., Oustry, F., Aitrami, M., A cone complementarity linearization algorithm for static output feedback and related problems (1997) IEEE Trans. Autom. Control, 42 (8), pp. 1171-1176. , 10.1109/9.618250 0018-9286Bernussou, J., Geromel, J.C., Korogui, R.H., On robust output feedback control for polytopic systems (2005) IEEE CDC-ECC '05, pp. 5018-5023. , 44thDe Oliveira, M.C., Bernussou, J., Geromel, J.C., A new discrete-time robust stability condition (1999) Syst. Control Lett., 37 (4), pp. 261-265. , 10.1016/S0167-6911(99)00035-3 0167-6911Scherer, C., Mixed H2/H∞ control (1995) Trends in Control - A European Perspective, , Isidori A. Springer, LondonGeromel, J.C., Palhares, A.G.B., (2004) Análise Linear de Sistemas Dinâmicos: Teoria, Ensaios Práticos e Exercícios' (In Portuguese), , Editora Edgard Blucher LTDA, São Paulo, BrazilVeillette, R.J., Medanić, J.V., Perkins, W.R., Design of reliable control systems (1992) IEEE Trans. Autom. Control, 37 (3), pp. 290-304. , 10.1109/9.119629 0018-928