Robust stabilization withH∞performance for a class of linear parameter-dependent systems

We focus on the issue of robust stabilization with H∞ performance for a class of linear time-invariant parameter-dependent systems under norm-bounded nonlinear uncertainties. By combining the idea of polynomially parameter-dependent quadratic Lyapunov functions and linear matrix inequalities formulations, some parameter-independent conditions with high precision are given to guarantee robust asymptotic stability and robust disturbance attenuation of the linear time-invariant parameter-dependent system in the presence of norm-bounded nonlinear uncertainties. The parameter-dependent state-feedback control is designed based on the Hamilton-Jacobi-Isaac (HJI) method. The applicability of the proposed design method is illustrated in a simple example.

[1]  S. Bittanti,et al.  Affine Parameter-Dependent Lyapunov Functions and Real Parametric Uncertainty , 1996 .

[2]  Fen Wu,et al.  Control design of switched LPV systems using multiple parameter-dependent Lyapunov functions , 2004, Proceedings of the 2004 American Control Conference.

[3]  L. Wang,et al.  Robust disturbance attenuation with stability for linear systems with norm-bounded nonlinear uncertainties , 1996, IEEE Trans. Autom. Control..

[4]  Tetsuya Iwasaki,et al.  Parameter-dependent Lyapunov function for exact stability analysis of single-parameter dependent LTI systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[5]  P. Khargonekar,et al.  Robust stabilization of linear systems with norm-bounded time-varying uncertainty , 1988 .

[6]  P. Bliman,et al.  LMI approach to spectral stabilizability of linear delay systems and stabilizability of linear systems-with, complex parameter , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[7]  Gary J. Balas,et al.  Design of Nonlinear Controllers for Active Vehicle Suspensions Using Parameter-Varying Control Synthesis , 2000 .

[8]  Pierre-Alexandre Bliman,et al.  A Convex Approach to Robust Stability for Linear Systems with Uncertain Scalar Parameters , 2003, SIAM J. Control. Optim..

[9]  Lihua Xie,et al.  Robust Kalman filtering for uncertain systems , 1994 .

[10]  Pierre-Alexandre Bliman,et al.  An existence result for polynomial solutions of parameter-dependent LMIs , 2004, Syst. Control. Lett..

[11]  Graziano Chesi,et al.  Polynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems: an LMI approach , 2005, IEEE Transactions on Automatic Control.

[12]  B. Lohmann,et al.  H∞ control of parameter-dependent state-delayed systems using polynomial parameter-dependent quadratic functions , 2005 .

[13]  E. Feron,et al.  Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions , 1996, IEEE Trans. Autom. Control..

[14]  V. Verdult.  Non linear system identification : a state-space approach , 2002 .

[15]  Gary J. Balas,et al.  Flight control of a tailless aircraft via linear parameter-varying techniques , 1999 .

[16]  Pierre-Alexandre Bliman.  Stabilization of LPV systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).