Design of Tracking Controller for Nonlinear Switched Systems with Time Delay in the Control Input and the States of the System

This paper proposes a desire tracking controller for nonlinear time varying switched systems in two modes. In the first mode, some subsystems are stable and in the second mode, some subsystems are unstable. Moreover, it is assumed that the time delay exists in the control input and the states of the system. In order to solve the proposed tracking control, several assumptions and conditions are considered. Besides, by using a new Lyapunov Krasovskii functional, the upper bound of the time delay for the global exponential stability of the proposed switched system is obtained as follows, Firstly, with the stable subsystems and secondly, with some unstable subsystems. Finally, a new tracking controller is designed for two modes. At the end, a numerical example is presented to show the effectiveness of our method.