The stability analysis of nonlinear switched systems with time delay in input and states with stable and unstable subsystems

Time delay and sampling appear in many industrial systems. It is irrefutable that applying measurement delay with controls can cause the sampling of control laws with the delay in the behavior of nonlinear control systems. As a result, in this paper, the stability of nonlinear time varying switched system with time delay in the input and the states of the system is studied in two modes by a new Lyapunov Krasovskii functional (LKF). Firstly, if all subsystems of the proposed nonlinear switched system with time delay are stable. Then, if some of the subsystems of the proposed switched system are unstable. This paper is organized in two steps. In the first step, the upper bound for the time delay under sufficient conditions in the nonlinear systems with time delay in input and states is obtained. In this step, the Uniformly Globally Asymptotic Stability is proved for nonlinear systems with the presence of time delay. In the second step, with a proper Lyapunov Krasovskii functional, the global exponential stability of the proposed switched system is proved. Also, finally a proper observer is designed for our proposed switched system in two stable and unstable modes.