Finite-time stability and stabilization for highly nonlinear stochastic Markov jump systems

Abstract

The research on finite-time stability (FTS) mainly focuses on linear and nonlinear systems, however, there are few studies on such problems for highly nonlinear systems. At present, most studies on FTS use the Lyapunov function method, and most of the results not only require the Lyapunov function in different modes to have the same feature, but also require the diffusion operators in different modes to be constrained by the same type of functions. This is somewhat restrictive to the selection of the Lyapunov function. Based on this, this paper concerns with FTS and asynchronous control of highly nonlinear stochastic Markov jump systems (HNSMJSs). Firstly, the criteria of $m$th moment finite-time stability ($m$-MFTS) for HNSMJSs in Lyapunov function form and parameter form are given and the asynchronous controller is provided to guarantee the $m$th moment finite-time stabilization ($m$-MFT stabilization). Moreover, HNSMJSs with deterministic time delay are extended to that with time-varying delay, and a more general result is given. Finally, three examples are provided to clarify the effectiveness of the proposed work.