Reachability-Guaranteed Sliding-Mode Control for Asynchronously Switched Uncertain Systems

In the sliding-mode control of switched systems, the mode-dependent sliding surface is generally considered to fulfill performance requirements of different subsystems. However, in the mode-dependent sliding surface design, the system state may oscillate among subsliding surfaces, which affects both stability and robustness. To solve this issue, this article starts from ensuring the reachability of each subsliding surface and proposes the reachability-guaranteed sliding-mode control for asynchronously switched uncertain systems. First, a type of asynchronous mode-dependent sliding surface is designed. Then, the control law is novelly proposed upon the allowable maximum settling time based on the fixed-time theory, and a new criterion is given to address the reachability of each subsliding surface within the mode-running interval. Stability is analyzed for the closed-loop system under restricted switchings, and solvable inequalities are presented for the optimization of the controller gain. Finally, implementation to the Chua's circuit validates superiorities of the proposed method.