Incremental dissipative control for nonlinear stochastic Markovian jump systems

Abstract This paper investigates the incremental dissipative control problem for nonlinear stochastic Markovian jump systems (MJSs) driven by the Markov process, Brownian motion, and disturbance-dependent noise. A stochastic version of incremental dissipativity for Markovian jump processes is presented, where incremental Lyapunov functions and a state dissipation inequality in expectation are used. Furthermore, the sufficient conditions of stochastic incremental dissipativity for nonlinear stochastic MJSs are given in terms of a set of coupled incremental Hamilton-Jacobi inequalities (iHJIs). Also, the incrementally globally asymptotically stable in the mean (IGASiM) conditions for nonlinear stochastic MJSs are derived by using stochastic incremental dissipativity. The sufficient conditions for the stochastic state-feedback incremental H ∞ control problem are obtained by solving a set of coupled iHJIs and by resorting to multiple Lyapunov functions. Two numerical examples demonstrated the effectiveness of the proposed method.