New stabilization criteria for time-delayed bimodal piecewise linear systems

Abstract

In this paper, we study the stability and stabilization of time-delayed bimodal piecewise linear systems via smooth Lyapunov-Krasovskii functionals. The main contributions of the paper are twofold: (1) a new stability criterion based on the proposed smooth Lyapunov-Krasovskii functional is derived to guarantee asymptotic stability in the case of zero inputs and (2) an interesting condition is proposed to design linear state feedback controllers to stabilize the system which is less conservative than those previously reported in the literature. Finally, some numerical examples illustrate the effectiveness of proposed methods.