Delay-dependent model reduction for continuous-time switched state-delayed systems

Abstract

<jats:title>Abstract</jats:title><jats:p>This paper studies the problem of exponential <jats:italic>H</jats:italic><jats:sub>∞</jats:sub> model reduction for continuous‐time switched delay system under average dwell time (ADT) switching signals. Time delay under consideration is interval time varying. Our attention is focused on the construction of the desired reduced order models, which guarantee that the resulting error systems under ADT switching signals are exponentially stable with an <jats:italic>H</jats:italic><jats:sub>∞</jats:sub> norm bound. By introducing a block matrix and making use of the ADT approach, delay‐dependent sufficient conditions for the existence of reduced order models are derived and formulated in terms of strict linear matrix inequalities (LMIs). Owing to the absence of non‐convex constraints, it is tractable to construct an admissible reduced order model. The effectiveness of the proposed methods is illustrated via two numerical examples. Copyright © 2011 John Wiley &amp; Sons, Ltd.</jats:p>