Generalized Filippov Solution in Stability Analysis and Stabilization of Piecewise Continuous Time-delay Systems

To analyze and synthesize time-delay systems with discontinuity, formulations of Filippov solution and associated essential principles in terms of sliding motion solution for differential inclusion systems are presented with respect to functional differential inclusion systems. Under the proposed theoretical framework, stability conditions and feedback stabilization approach are proposed for functional differential inclusion systems with set-valued analysis tools. A numerical example is given to illustrate the proposed framework for piecewise continuous time-delay systems.