Robust static output feedback H∞ control design for linear systems with polytopic uncertainties

Abstract This paper investigates the problem of robust static output feedback H ∞ control for linear systems with polytopic uncertainties. A new method is proposed for robust static output feedback H ∞ controller design. The proposed design method is applicable for general uncertain systems, without the need to impose any constraints on system matrices. The corresponding design conditions are presented in the form of linear matrix inequalities (LMIs). One of the advantages of the new method lies in its less conservatism. The proposed design method is also applicable to both continuous-time and discrete-time systems. The performance of the method is compared with other methods based on several examples.

[1]  Dimitri Peaucelle,et al.  Robust Static Output Feedback Stabilization for Polytopic Uncertain Systems: Improving the Guaranteed Performance Bound , 2003 .

[2]  Guang-Hong Yang,et al.  New Results on Output Feedback $H_{\infty} $ Control for Linear Discrete-Time Systems , 2014, IEEE Transactions on Automatic Control.

[3]  Robert E. Benton,et al.  A non-iterative LMI-based algorithm for robust static-output-feedback stabilization , 1999 .

[4]  J. Geromel,et al.  Extended H 2 and H norm characterizations and controller parametrizations for discrete-time systems , 2002 .

[5]  Shengyuan Xu,et al.  Robust H∞ control for uncertain discrete-time systems with time-varying delays via exponential output feedback controllers , 2004, Syst. Control. Lett..

[6]  J. Tsitsiklis,et al.  NP-hardness of some linear control design problems , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[7]  Uri Shaked,et al.  Robust Reduced-order Output-feedback H∞ Control , 2009 .

[8]  Thierry-Marie Guerra,et al.  Continuous Takagi–Sugeno's Models: Reduction of the Number of LMI Conditions in Various Fuzzy Control Design Technics , 2007, IEEE Transactions on Fuzzy Systems.

[9]  Huijun Gao,et al.  A Parameter-Dependent Approach to Robust $H_{\infty }$ Filtering for Time-Delay Systems , 2008, IEEE Transactions on Automatic Control.

[10]  Alexandre Trofino,et al.  Sufficient LMI conditions for output feedback control problems , 1999, IEEE Trans. Autom. Control..

[11]  Uri Shaked,et al.  An LPD approach to robust H2 and H∞ static output-feedback design , 2003, IEEE Trans. Autom. Control..

[12]  Michel Verhaegen,et al.  Robust output-feedback controller design via local BMI optimization , 2004, Autom..

[13]  P. Gahinet,et al.  A linear matrix inequality approach to H∞ control , 1994 .

[14]  Zidong Wang,et al.  RobustH∞ Finite-HorizonFilteringwithRandomly OccurredNonlinearitiesandQuantizationEffects ⋆ , 2010 .

[15]  Uri Shaked,et al.  Static H2 and H∞ output-feedback of discrete-time LTI systems with state multiplicative noise , 2006, Syst. Control. Lett..

[16]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in System and Control Theory , 1994, Studies in Applied Mathematics.

[17]  David Zhang,et al.  Improved robust H2 and Hinfinity filtering for uncertain discrete-time systems , 2004, Autom..

[18]  J. Geromel,et al.  A new discrete-time robust stability condition , 1999 .

[19]  Goele Pipeleers,et al.  Reduced-order multi-objective ℋ∞ control of an overhead crane test setup , 2013, 52nd IEEE Conference on Decision and Control.

[20]  Guang-Hong Yang,et al.  Robust static output feedback control for linear discrete-time systems with time-varying uncertainties , 2008, Syst. Control. Lett..

[21]  Guang-Hong Yang,et al.  Robust static output feedback control synthesis for linear continuous systems with polytopic uncertainties , 2013, Autom..

[22]  C. M. Agulhari,et al.  Robust ℋ∞ static output-feedback design for time-invariant discrete-time polytopic systems from parameter-dependent state-feedback gains , 2010, Proceedings of the 2010 American Control Conference.

[23]  Zidong Wang,et al.  Robust Hinfinity finite-horizon filtering with randomly occurred nonlinearities and quantization effects , 2010, Autom..

[24]  Shengyuan Xu,et al.  Technical communique: New results on delay-dependent robust H∞ control for systems with time-varying delays , 2006 .

[25]  Friedemann Leibfritz,et al.  An LMI-Based Algorithm for Designing Suboptimal Static H2/Hinfinity Output Feedback Controllers , 2000, SIAM J. Control. Optim..

[26]  Lihua Xie,et al.  Robust H/sub 2/ and H/sub /spl infin// control of discrete-time systems with polytopic uncertainties via dynamic output feedback , 2005, Proceedings of the 2005, American Control Conference, 2005..

[27]  Ricardo C. L. F. Oliveira,et al.  H∞ Guaranteed Cost Computation by Means of Parameter Dependent Lyapunov Functions , 2003 .

[28]  Huijun Gao,et al.  A new design of robust H2 filters for uncertain systems , 2008, Syst. Control. Lett..

[29]  Ricardo C. L. F. Oliveira,et al.  I guaranteed cost computation by means of parameter-dependent Lyapunov functions , 2004, Autom..

[30]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[31]  Olivier Bachelier,et al.  Static output feedback design for uncertain linear discrete time systems , 2004, IMA J. Math. Control. Inf..

[32]  Ricardo C. L. F. Oliveira,et al.  LMI Relaxations for Reduced-Order Robust ${\cal H}_{\infty}$ Control of Continuous-Time Uncertain Linear Systems , 2012, IEEE Transactions on Automatic Control.

[33]  Hui Zhang,et al.  Robust Static Output Feedback Control and Remote PID Design for Networked Motor Systems , 2011, IEEE Transactions on Industrial Electronics.

[34]  M. C. D. Oliveiraa,et al.  A new discrete-time robust stability condition ( , 1999 .