Stabilization Optimal Control for Itô Stochastic Markov Jump System with Indefinite State

The paper focuses on the optimal control and stabilization of indefinite stochastic Markov jump systems with multiplicative noise. The sufficient and necessary condition of stabilization for Ito Markov jump system is given by the generalized algebraic Riccati equation (GARE). One of the key techniques is that extending the equivalence between the GARE and singular algebraic Riccati equation (SARE) into the system with jumping parameters. By the Lyapunov function, the stabilization problem under general uncertainty is transformed into the stability analysis under certain conditions. For the infinite-horizon case, the necessary and sufficient condition for the mean square stabilization of Itô stochastic Markov jump system in the mean square sense is obtained. Moreover, the cost functional of this system and it’s optimal controller are developed.