Extended hybrid control scheme for asynchronous switching

This paper is devoted to the problem of extended hybrid control for asynchronous switching between system modes (we call each subsystem a mode) and controller candidates. Such undesirable behavior is caused by mismatch delay. Since asynchronous switching is relevant in many switched systems, this paper presents highly impressive results in stabilizing and controlling a switched linear system infected by mismatch delay. In this technical note, an asynchronous switched system is considered as a switched system with new stable and unstable subsystems. Through piecewise Lyapunov-like function (LLF) approach, two different mode-dependent dwell time (MDT) structures are designed. These dwell time structures satisfy a lower bound and an upper bound for stable and unstable part of each controlled subsystem respectively. In this regard, a hybrid control scheme with L₂-gain stability analysis is provided for the mentioned system to cover the mismatch defect. The obtained boundary conditions can be incorporated with the synthesis problem in convex formation. Besides, to have more satisfying results, a rest supervisor is also considered to enforce the reset rules to the controller candidates. By determining acceptable dwell time parameters, the controller gain matrices of the new approach will be calculated to solve linear matrix inequality (LMI) optimization. Finally, the effectiveness of the obtained theoretical results is demonstrated via a numerical example.