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.

本文研究了可靠的^ h _∞在随机控制延迟马尔可夫跳变系统（SDMJSs）异步跳下执行器故障，不确定的升学率（TRS）。假设执行器故障是在马尔可夫过程下随机发生的，其跳跃模式与系统的跳跃模式不同。成功建立了具有混合异步马尔可夫跳跃模式（AMJM）的闭环SDMJS的通用函数Itô公式。由广义官能伊藤式和混合模式依赖性Lyapunov函数，可靠的足够的延迟依赖病症ħ _∞通过矩阵操作和松弛方法，提出了带有混合AMJM的SDMJS的控制器设计。最后，以VTOL（垂直起降）直升机系统为例，论证了所提出的控制器设计方案的可行性和有效性。