Global exponential stabilization of language constrained switched linear discrete-time system based on the s-procedure approach

This paper considers global exponential stabilization (GES) of switched linear discrete-time system under language constraint which is generated by non-deterministic finite state automata. A technique in linear matrix inequalities called S-procedure is employed to provide sufficient conditions of GES which are less conservative than the existing Lyapunov-Metzler condition. Moreover, by revising the construction of Lyapunov matrices and the corresponding switching control policy, a more flexible result is obtained such that stabilization path at each moment might be multiple. Finally, a numerical example is given to illustrate the effectiveness of the proposed results.