Reliable H∞ Control on Stochastic Delayed Markovian Jump System with Asynchronous Jumped Actuator Failure

Abstract

This paper studies the reliable H∞ control on stochastic delayed Markovian jump systems (SDMJSs) with asynchronous jumped actuator failure and uncertain transition rates (TRs). It is assumed that the actuator failure occurs randomly under a Markov process with its jumping mode different from the system’s one. A generalized functional Ito’s formula for the closed-loop SDMJSs with mixed asynchronous Markovian jump modes (AMJMs) is successfully established. By the generalized functional Ito’s formula and the mixed-mode-dependent Lyapunov functionals, a sufficient delay-dependent condition of the reliable H∞ controller design for the SDMJSs with mixed AMJMs is proposed via matrix manipulation and a relaxation method. Finally, an example on VTOL (vertical take-off and landing) helicopter system is given to demonstrate the feasibility and effectiveness of the presented controller design scheme.