Robust stability and stabilization of uncertain stochastic systems involving jump random noise

Abstract

Stochastic system involving jump random noise (RN) is considered in this paper. By employing Poisson process (PP) to depict jump RN, this paper investigates the robust stability and stabilization problem of uncertain stochastic systems involving Poisson process (SSIPPs). Firstly, noting that the model of the SSIPP is a stochastic differential equation (SDE) involving semimartingale, we utilize stochastic analysis to transform the SSIPP into an SDE involving martingale so that we can use martingale theory to investigate such kind of stochastic systems (SSs). Secondly, on basis of stochastic theory and Lyapunov theory, this paper presents a robust stability criterion and designs a state feedback controller for the uncertain SSIPP. Finally, a numerical example is given to check the effectiveness of the derived results.