Further results on fixed‐time stability of time‐varying hybrid systems

Abstract The introduction of time‐varying factors makes it difficult and complex to study the stability of hybrid systems. How to improve the traditional stability analysis method to study the stability of time‐varying hybrid systems is a great challenge. In this paper, the fixed‐time stability (FxTS) of time‐varying hybrid systems is investigated. Starting with time‐varying nonlinear systems, two relaxed stability conditions are proposed to verify the FxTS of systems by using the time‐varying Lyapunov functions. Then, the obtained results are extended to study the FxTS of time‐varying hybrid systems, some improved stability conditions are given by combining the methods of minimum dwell time and multiple time‐varying Lyapunov functions. Compared with the existing results, the obtained conditions are less conservative and provide the more accurate estimations for the convergence time of systems. Two numerical examples are given to illustrate the theoretical results.