Finite-time stability and asynchronous H8 control for highly nonlinear hybrid stochastic systems

In this paper, the pth moment finite-time stochastic stability (p-MFTS stability) and asynchronous H-8 control for highly nonlinear hybrid stochastic systems (HNHSSs) are investigated. Firstly, the definition of p-MSFT stability for HNHSSs is proposed, and the stability criteria are given by the mode-dependent average dwell time (MDADT) method. Secondly, the asynchronous H-8 controller is designed to ensure that HNHSSs are pth moment finite-time stochastically stabilizable (p-MFTS stabilizable) and satisfy H-8 performance. When designing the asynchronous H-8 controller, deterministic asynchrony and stochastic asynchrony are considered simultaneously. Moreover, since the coefficients of HNHSSs have highly nonlinear structures without satisfying the linear growth condition (LGC), the Lyapunov function u and the operator Lu are bounded by polynomials of degree higher than p, which means that weaker conditions of p-MFTS stability are proposed. Finally, examples are presented to illustrate the availability of the results.