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Stability and performance analysis of time‐delay LPV systems with brief instability
Author(s) -
Mohammadpour Javad,
Grigoriadis Karolos
Publication year - 2011
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1633
Subject(s) - instability , parameterized complexity , control theory (sociology) , linear matrix inequality , computer science , nonlinear system , linear system , stability (learning theory) , norm (philosophy) , fault detection and isolation , exponential stability , mathematics , mathematical optimization , control (management) , algorithm , actuator , mathematical analysis , physics , quantum mechanics , artificial intelligence , machine learning , mechanics , political science , law
Linear 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 ℒ 2 ‐gain (or so‐called ℋ ∞ 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 ℋ ∞ 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.