Stability and performance analysis of time‐delay LPV systems with brief instability

Abstract

AbstractLinear parameter‐varying (LPV) systems provide a systematic framework for the study of nonlinear systems by considering a representative family of linear time‐invariant systems parameterized by system parameters residing in a compact set. The brief instability concept in such systems allows the linear system to be unstable for some trajectories of the LPV parameter set, so that instability occurs only for short periods of time. In the present paper, we extend the notion of brief instability to LPV systems with time delay in their dynamics. The results provide tools for the stability and performance analysis of such systems, where performance is evaluated in terms of induced ℒ︁2‐gain (or so‐called ℋ︁∞ norm). The main results of this paper illustrate that stability and performance conditions can be evaluated by examining the feasibility of parameterized sets of linear matrix inequalities (LMIs). Using the results of this paper, we then investigate analysis conditions to guarantee the asymptotic stability and ℋ︁∞ performance of fault‐tolerant control (FTC) systems, in which instability may take place for a short period of time due to the false identification of the fault signals provided by a fault detection and isolation (FDI) module. The numerical examples are used to illustrate the qualification of the proposed analysis and synthesis results for addressing brief instability in time‐delay systems. Copyright © 2010 John Wiley & Sons, Ltd.