Control for Mixed-Mode Based Switched Nonlinear Systems with Time-Varying Delay

This paper investigated performance of the switched nonlinear systems with time-varying delay, which contains mixed modes, important characteristics of switched delay systems. Most of the references ignored the existence of mixed modes in such systems, which is a fatal mistake. This paper will correct the mistake of the existing references. The mixed modes give the control for switched nonlinear delay systems a challenge. With this difficulty, we take measures to handle the effects of mixed modes on such systems and achieve the performance of such systems. Firstly, the control analysis is divided into two cases, and the sufficient conditions for the exponential decay of the Lyapunov-Krasovskii functionals are given with the integral interval approach. Secondly, the combination of average dwell-time approach and subsystem activation rate is utilized to achieve the performance for the mixed-mode based switched systems with time-varying delay. Finally, simulation examples show the efficiency of the switching control strategy.