New stabilization of stochastic delayed jumping systems realized by a partially delay-dependent controller

This paper investigates the stabilization of stochastic delayed jumping systems by exploiting a kind of partially delay-dependent controller, where both non-delay and delay states are contained but happen asynchronously. Different from the traditionally stabilizing controller only having non-delay or delay states or containing both, the asynchronous occurring of non-delay and delay terms is modeled by the Bernoulli variable. The probability distribution of such two terms are considered in the controller design process. Based on the proposed model, sufficient conditions for the existence of such controllers are presented in terms of LMIs, which are closely related to the probabilities. Finally, a numerical example is exploited to show the effectiveness and superiority of the proposed methods.