New robust stability and performance conditions based on parameter dependent multipliers

This paper introduces a new robust stability and performance characterization for parameter dependent systems. The main idea is to jointly use parameter dependent Lyapunov functions and parameter dependent multipliers. It is shown that the novel tests can be easily specialized to the results that have been recently proposed in the literature and that have been derived in an independent fashion for discrete- and continuous-time systems. It is revealed that these characterization apply to system descriptions with rational parameter dependence, and we discuss in how far they extend to robust state-feedback controller synthesis. Various examples demonstrate the benefit of the proposed algorithms over previous approaches.

[1]  B. Barmish.  Necessary and sufficient conditions for quadratic stabilizability of an uncertain system , 1985 .

[2]  Andrew Packard,et al.  The complex structured singular value , 1993, Autom..

[3]  E. Feron,et al.  S-procedure for the analysis of control systems with parametric uncertainties via parameter-dependent Lyapunov functions , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[4]  Toshiharu Sugie,et al.  New upper bound of the real /spl mu/ based on the parameter dependent multiplier , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

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

[6]  C. Scherer,et al.  Robust stability analysis for parameter dependent systems using full block S-procedure , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[7]  Izumi Masubuchi,et al.  LMI-based controller synthesis: A unified formulation and solution , 1998 .

[8]  J. Geromel,et al.  Parameter dependant Lyapunov control design: numerical evaluation , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[9]  J. Geromel,et al.  An LMI optimization approach to multiobjective controller design for discrete-time systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

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

[11]  S. Dasgupta,et al.  Parametric Lyapunov functions for uncertain systems: the multiplier approach , 1999 .

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