Fixed-Time Stability of Time-Varying Hybrid Systems with Time-Delay

In this paper, fixed-time stability (FxTS) of time-varying (TV) hybrid systems with time-delay (TD) is investigated. Starting with TV nonlinear systems with TD, some sufficient conditions are given to verify the FxTS of systems by using TV Lyapunov–Krasovskii functional and integral technique. Then, the obtained results are extended to the case of hybrid systems, several FxTS conditions are provided by using the multiple TV Lyapunov–Krasovskii functional and the function-dependent minimum dwell time technique. Comparing with the existing results, the obtained results can provide the more accurate estimation of the convergence time of systems, and can be applied to a wider class of systems. Finally, two numerical examples are given to illustrate the theoretical results.