Stability analysis and robust tracking control for a class of switched nonlinear systems with uncertain input delay

Abstract

In this paper, the stability issue and tracking control problem for a class of switched nonlinear systems with uncertain input delay and disturbance are investigated. First, it is assumed a piecewise Lyapunov function exists for the nominal system (system without input delay and disturbance), and then, under the terms of the hypothetical piecewise Lyapunov function, a new Lyapunov-Krasovskii functional is constructed. By employing this new function and a switching signal which satisfies the average dwell time, the delay-dependent input-to-state stability under a certain delay bound is provided; also, a mechanism is invented to find the upper bound for input delay of switched system. In the next step, tracking control problem for this system is studied. Finally, a kind of state feedback control law which ensures conditions of aforesaid hypothetical piecewise Lyapunov function is proposed to guarantee the input-to-state stability and the robust model reference tracking performance. Simulation examples are given to illustrate the effectiveness of the proposed strategy.