Stabilization of continuous-time randomly switched systems via the LMI approach

This paper is concerned on the stabilization problem of continuous-time switched systems with random switching signal where the dwell time in each subsystem consists of a fixed part and random part. New sufficient conditions for stabilizing controllers including mode-independent case are provided in terms of LMIs, which could be solved directly. Moreover, the obtained results are extended to a more general case that the corresponding operation mode of a controller experiences a disordering phenomenon. Without designing a controller depending on new operation modes (NOMs), a kind of controller only depending on the original operation modes (OOMs) is proposed and satisfies a minimum variance approximation, whose solvable conditions are also with LMI forms. Finally, numerical examples are used to demonstrate the effectiveness of the proposed methods.