A direct characterization of L/sub 2/-gain controllers for LPV systems

In this paper, a class of linear parameter-dependent output feedback controllers that satisfy quadratic stability and an induced L/sub 2/-norm bound for a given linear parameter-varying (LPV) plant are considered. By using a parameter-independent common Lyapunov function, the solvability conditions are expressed in terms of finite-dimensional linear matrix inequalities (LMI's) evaluated at the extreme points of the admissible parameter set. Conditions under which strictly proper controllers can be used are obtained. By restricting some of the controller matrices to be constant, the input and output matrices can be parameter varying, without destroying the convexity of the problem. Cases where the controller matrices can be obtained without interpolation are also discussed, thereby simplifying the implementation of the controller. A numerical example is included which demonstrates the application of the results.

[1]  Pierre Apkarian,et al.  Self-scheduled H∞ control of linear parameter-varying systems: a design example , 1995, Autom..

[2]  Athanasios Sideris,et al.  H ∞ control with parametric Lyapunov functions , 1997 .

[3]  P. Gahinet,et al.  A convex characterization of gain-scheduled H∞ controllers , 1995, IEEE Trans. Autom. Control..

[4]  Fen Wu,et al.  Induced L2‐norm control for LPV systems with bounded parameter variation rates , 1996 .

[5]  P. Gahinet,et al.  Affine parameter-dependent Lyapunov functions for real parametric uncertainty , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[6]  A. Packard,et al.  Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback , 1994 .

[7]  William E. Schmitendorf,et al.  Design methodology for robust stabilizing controllers , 1987 .

[8]  A. Packard.  Gain scheduling via linear fractional transformations , 1994 .

[9]  I. Masubuchi,et al.  LMI-based output feedback controller design-using a convex parametrization of full-order controllers , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[10]  Existence conditions for a nonstandard H∞ problem , 1993, 1993 American Control Conference.

[11]  Tetsuya Iwasaki,et al.  All controllers for the general H∞ control problem: LMI existence conditions and state space formulas , 1994, Autom..

[12]  Mitsuji Sampei,et al.  An algebraic approach to H ∞ output feedback control problems , 1990 .

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

[14]  Lihua Xie,et al.  H/sub infinity / control and quadratic stabilization of systems with parameter uncertainty via output feedback , 1992 .

[15]  Jakob Stoustrup,et al.  Robust performance of systems with structured uncertainties in state space , 1995, Autom..

[16]  Michael Athans,et al.  Guaranteed properties of gain scheduled control for linear parameter-varying plants , 1991, Autom..