Exponential stability in mean square of a singularly perturbed linear stochastic system with state-multiplicative white-noise perturbations and Markovian switching

摘要

This study deals with a stabilisation problem for a class of singularly perturbed linear stochastic systems with state-multiplicative white-noise and Markovian jumping parameters. Based on the Lyapunov- type operator, an exponential stability in mean square is discussed intensively. First, after decomposing the full-order stochastic Lyapunov differential equations, the conditions that the reduced-order systems are both mean square stable are established. Second, it is shown that there exist small perturbation parameters that cause the original stochastic systems to be mean square stable. Moreover, it is also shown that the parameter-independent composite stabilising controller is established by solving the linear matrix inequalities.