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

This paper concerns H ∞ 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 H ∞ 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 H ∞ 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 & Sons, Ltd.