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

Wenpin Luo, Jun Yang*, and Xinzhi Liu
International Journal of Control, Automation, and Systems, vol. 19, no. 2, pp.618-631, 2021

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 Itô’s formula for the closed-loop SDMJSs with mixed asynchronous Markovian jump modes (AMJMs) is successfully established. By the generalized functional Itô’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.

Keyword : Asynchronous jumped actuator failure, functional Itô’s formula, Lyapunov functionals, reliable H∞ control, stability analysis, stochastic delayed Markovian jump systems (SDMJSs).

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