Slack variable approach for robust stability analysis of switching discrete-time systems

Robust stability analysis is investigated for discrete-time linear systems with rational dependency with respect to polytopic type uncertainties. Two type of uncertainties are considered: constant parametric uncertainties and timevarying switching uncertainties. Results are in LMI formalism and proofs involve parameter-dependent, quadratic in the state, Lyapunov functions. The new proposed conditions are shown to extend and merge two important existing results. Conservatism reduction is tackled via a model augmentation technique. Numerical complexity is contained by exploiting the structure of the models with respect to the uncertainties.

[1]  Gabriela Iuliana Bara.  Dilated LMI conditions for time-varying polytopic descriptor systems: the discrete-time case , 2011, Int. J. Control.

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

[3]  Maurício C. de Oliveira,et al.  A class of robust stability conditions where linear parameter dependence of the Lyapunov function is a necessary condition for arbitrary parameter dependence , 2005, Syst. Control. Lett..

[4]  Minyue Fu,et al.  Guaranteed cost control of uncertain nonlinear systems via polynomial lyapunov functions , 2002, IEEE Trans. Autom. Control..

[5]  Jamal Daafouz,et al.  Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach , 2002, IEEE Trans. Autom. Control..

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

[7]  Jamal Daafouz,et al.  Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties , 2001, Syst. Control. Lett..

[8]  D. Peaucelle,et al.  Robust Performance Analysis of Linear Time-Invariant Uncertain Systems by Taking Higher-Order Time-Derivatives of the State , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[9]  J. Doyle,et al.  Review of LFTs, LMIs, and mu. [Linear Fractional Transformations, Linear Matrix Inequalities , 1991 .

[10]  D. Henrion,et al.  QUADRATIC SEPARATION FOR FEEDBACK CONNECTION OF AN UNCERTAIN MATRIX AND AN IMPLICIT LINEAR TRANSFORMATION , 2005 .

[11]  Kim-Chuan Toh,et al.  SDPT3 -- A Matlab Software Package for Semidefinite Programming , 1996 .

[12]  Carlos E. de Souza,et al.  Robust stability of discrete-time linear descriptor systems with time-varying uncertainties via parametric Lyapunov function , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[13]  Dimitri Peaucelle,et al.  Integral Quadratic Separation Applied to Polytopic Systems , 2009 .

[14]  Masami Saeki,et al.  Synthesis of output feedback gain-scheduling controllers based on descriptor LPV system representation , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[15]  J. Bernussou,et al.  A new robust D-stability condition for real convex polytopic uncertainty , 2000 .

[16]  Liu Hsu,et al.  LMI characterization of structural and robust stability , 1998 .