Quantitative Mean Square Exponential Stability and Stabilization of Linear Itô Stochastic Markovian Jump Systems Driven by Both Brownian and Poisson Noises

Abstract

In this paper, quantitative mean square exponential stability and stabilization of Itô-type linear stochastic Markovian jump systems with Brownian and Poisson noises are investigated. First, the definition of quantitative mean square exponential stability, which takes into account the transient and steady behaviors of the system, is presented. Second, the relationship between general finite-time mean square stability, finite-time stochastic stability, and quantitative mean square exponential stability is proposed. Subsequently, some sufficient conditions for the existence of state feedback and observer-based controllers are derived, and an algorithm is offered to solve the matrix inequalities resulting from quantitative mean square exponential stabilization. Finally, the effectiveness of the proposed results is illustrated with the numerical example and the practical example.