Robust finite-time H2/H∞ control for stochastic Markovian jump systems via state feedback

Abstract

The robust finite-time [Formula: see text] control problems for linear discrete-time stochastic Markovian jump systems (MJSs) with external disturbance are investigated. Firstly, the definitions of robust finite-time boundedness, and robust finite-time [Formula: see text] boundedness are presented. Subsequently, by using the stochastic Lyapunov–Krasovskii functional method and linear matrix inequality technique, sufficient conditions for the existence of a robust finite-time [Formula: see text] controller are provided for stochastic MJSs. A state feedback controller is designed. Furthermore, the finite-time guaranteed cost bounds are given. More specifically, the designed controller not only ensures the finite-time [Formula: see text] bounded but also makes the [Formula: see text] cost function less than the bound given by the performance index of the systems. Finally, two examples are given to illustrate the validity of the proposed approach.