Finite-time H ∞ control for stochastic Markovian jump systems with time-varying delay and generally uncertain transition rates

Abstract

This paper considers the finite-time control problem for Markovian jump systems (MJSs) with time-varying delay and generally uncertain transition rates (GUTRs). Based on Lyapunov-Krasovskii functionals and free-weight matrices, some sufficient conditions for finite-time boundedness and finite-time boundedness of MJSs are derived in the presence of external disturbances and It-type stochastic disturbances. A state feedback controller is proposed to achieve finite-time boundedness performance. By applying linear matrix inequalities (LMIs), the parameterisation of the controller is converted to a convex optimisation problem. Finally, a practical example demonstrates the effectiveness of the proposed method.