Stochastic stability and stabilization for stochastic differential semi‐Markov jump systems with incremental quadratic constraints

Abstract

AbstractThe problem of the stochastic stability analysis and state feedback stabilization for nonlinear stochastic differential semi‐Markov jump systems with incremental quadratic constraints is investigated in this article. Different from Markovian process, the transition rate is time varying with known bounds and the sojourn time is conformed to the Weibull distribution in semi‐Markov process. Traditional nonlinear constraint such as Lipschitz, one‐sided Lipschitz, and so forth, is extended to incremental quadratic constraint. By the mode‐dependent Lyapunov function and the slack variable method, the sufficient conditions ensuring that the considered systems are stochastically stable are formulated by linear matrix inequalities. Then, a state feedback controller is designed to drive the closed‐loop system stochastically stable. Finally, an example of helicopter is used to illustrate the superiority as well as effectiveness of the results in this treatise.