Fixed-Time Stabilization for Interconnected Systems with Discontinuous Interconnections and Nonidentical Perturbations

Abstract

This paper investigates the fixed-time stabilization issue for a class of nonlinear interconnected systems with discontinuous interconnections and nonidentical perturbations. Firstly, according to the differential inclusion theory, the solutions of such discontinuous interconnected system are defined in the sense of Filippov. In addition, an improved fixed-time lemma, in which the regional bound r can be freely chosen in [0, 1], is proposed to realize the fixed-time stabilization and estimate the settling time. Then, through designing a state feedback controller and utilizing generalized Lyapunov functional method, sufficient criteria are derived to guarantee the fixed-time stabilization of the discontinuous interconnected system. Especially, the upper bound of the convergence time is estimated by a fixed time, which is independent of initial conditions. Finally, the proposed methodology and results are verified by an example.