A µ-dependent approach to H∞ control of uncertain switched linear systems with average dwell time

Abstract

<jats:title>Abstract</jats:title><jats:p>This paper concerns <jats:italic>H</jats:italic><jats:sub>∞</jats:sub> control problem for a class of discrete‐time uncertain switched linear systems with average dwell time. The stability result for general discrete‐time switched systems is first explored, and a µ‐dependent approach is then introduced for the considered systems to the <jats:italic>H</jats:italic><jats:sub>∞</jats:sub> controller solution. A mode‐dependent state‐feedback controller is designed such that the resulting closed‐loop system is robust exponentially stable and has a prescribed exponential <jats:italic>H</jats:italic><jats:sub>∞</jats:sub> performance index. The µ‐dependent existence conditions of desired controller and admissible switching signals are derived and formulated in terms of linear matrix inequalities (LMIs). A numerical example is given to demonstrate the effectiveness of the developed theoretical results. Copyright © 2009 John Wiley &amp; Sons, Ltd.</jats:p>