Finite-time stability and stabilization of stochastic delayed jump systems via general controllers

This paper deals with the finite-time stability and stabilization problems of stochastic delayed jump systems, where the stabilization is realized by some general controllers. Firstly, two respective conditions are proposed to check its finite-time stability, which are different from some existing methods. Based on the proposed results, sufficient conditions for the existence of a new kind of partially delay-dependent controller are provided with LMIs, which contain non-delay and delay states together but occur asynchronously. It is seen that the presented results are very close to the probability distributions of non-delay and delay states. Moreover, the key idea of the proposed controller is extended to other general cases that the desired controller has been added to the drift and diffusion sections with some probabilities or experiences disorder phenomenon. Finally, numerical examples are exploited to demonstrate the effectiveness and superiority of the proposed methods.