Equivalence of several stability conditions for switched linear systems with dwell time

Abstract

SummaryIn this paper, several equivalent stability conditions for switched linear systems with dwell time are presented. Both continuous‐time and discrete‐time cases are considered. For the continuous‐time case, the conditions that are convex in system matrices are presented in terms of infinite‐dimensional linear matrix inequalities (LMIs), which are not numerically testable. Then, by adopting the sum of square (SOS) and piecewise linear approach, computable conditions are formulated in terms of SOS program and LMIs. Compared to the literature, less conservative results can be obtained through solving these conditions for the same polynomial degree or discretized order. For the discrete‐time case, the stability conditions, which are convex in system matrices, are numerically testable. The convexity comes at the price of increment of computational complexity. Furthermore, by adopting the convexification approach, sufficient stability conditions of switched linear systems with polytopic uncertainties are derived, both for continuous‐time and discrete‐time cases. At last, several examples are given to demonstrate the correctness and advantages of our results.