Robust stability analysis of linear systems with affine parameter uncertainties

Authors:	Yang Guang-Hong, National University of Singapore, Singapore Lum Kai-Yew, National University of Singapore, Singapore
Topic:	2.5 Robust Control
Session:	Parametric Robustness
Keywords:	Linear systems, robust stability, parameter-dependent Lyapunov function, LMI, parameter uncertainty

Abstract

This paper is concerned with the problem of robust stability of a class of uncertain linear systems,where the system state-matrices considered are affinely dependent on the uncertain parameters. Affine parameter-dependent Lyapunov functions are exploited to prove stability, and a robust stability criterion for the above class of systems to be affinely quadratically stable (AQS) is given in terms of linear matrix inequalities (LMIs). A comparison with the existing tests for AQS is given, and it is shown that the robust stability criterion provides a test that is not more conservative than the existing tests. Numerical examples are given to illustrate the results.