Exponential Stabilizability Analysis for Constrained Switched System

This paper considers the global exponential stabilizability (GES) of a switched linear system under language constraints, which can be described by a nondeterministic finite state automaton. Firstly, the automaton is represented as a labeled diagraph to reduce the problem to the GES analysis in strongly connected components. Secondly, we analysis the properties of the lifted labeled diagraph, which can express the dwell time constraints intuitively. Based on the lifted labeled diagraph, we generalize the Lyapunov-Metzler condition to an M-step version, and propose a less conservative condition based on S-procedure. Finally, a numerical example is provided to demonstrate the S-procedure condition.