Functional differential inclusion-based approach to control of discontinuous nonlinear systems with time delay

This paper presents functional differential inclusion based approach to investigate the stabilization of discontinuous nonlinear systems with time delay. First, the conception of Filippov solution for ordinary differential equations with discontinuous right-hand side is extended to discontinuous systems with time delay, which is a solution of functional differential inclusions determined by the Filippov set-valued functional. With this conception and the strong stability, it is shown that the Lyapunov stability framework can be easily extended to discontinuous systems with time delay. Then, the feedback stabilization problem for a class of discontinuous nonlinear systems with time delay is investigated with the proposed functional differential inclusion-based framework. It is shown that for the systems, a stabilization controller can be provided by a by means of a system-related function satisfying HJI inequality. Finally, to demonstrate the design process of the proposed approach, an application example with automotive system background is addressed.