Absolute exponential stability of switched nonlinear time-delay systems

This paper investigates absolute exponential stability of switched nonlinear time-delay systems in both continuous-time and discrete-time contexts. The nonlinearities of the systems satisfy a certain sector condition. First, an improved Lyapunov-Krasovskii functional of switched nonlinear time-delay systems in the continuous-time form is constructed. By using the multiple Lyapunov-Krasovskii functionals and average dwell time switching approaches, two less conservative sufficient conditions for the absolute exponential stability of the systems with single/multiple delays are established, respectively. Then, the obtained results are extended to discrete-time systems. All proposed conditions are described via linear programming. By some comparisons, it is shown that the results in the paper are less conservative than those in the literature. Finally, two examples are given to show the effectiveness of the theoretical findings.