Optimal Control and Stabilization for Discrete-time Markov Jump Systems with Indefinite Weight Costs with Multi-channel Multiplicative Noise

摘要

This paper mainly investigates the optimal control and stabilization problems for discrete-time Markov jump systems with multi-channel multiplicative noise. we use the diagonal matrixes to represent multi-channel multiplicative noise. Bedides, the weighting matrices in the performance index, which are with regard to both of state and control are allowed to be indefinite. In addition, the conditions for that the optimal controller exists in finite-horizon are given from generalized difference Riccati equations explicitly. It’s proposed that the discrete-time Markov jump linear system is mean square stabilizable if and only if the generalized algebraic Riccati equations with Markov jump has a solution, which is also the maximal solution to generalized algebraic Riccati equation with Markov jump. What’s more, a Lyapunov function is defined by means of the optimal performance index to simplify the stabilization problem in indefinite-horizon to the definite case.