On Exponential Stability of Switched Systems with Delay: Lyapunov Function Approach

The switched dynamical system consisting of two linear subsystems with delay is considered. The problem is to find conditions guaranteeing exponential stability of the system for any switching sequence. Combining with Halanay differential inequality, both quadratic and piecewise quadratic construction of Lyapunov function is exploited, from which the stability criteria in terms of linear matrix inequalities are derived. Furthermore, it is strictly verified that the exponential decay rate holds uniformly for all switching sequence, and is definitely determined by the structure of subsystems. Numerical examples are given to demonstrate the effectiveness of our results.