This paper is dedicated to the asynchronous H_∞ output feedback control for a class of discrete-time uncertain singular stochastic Markov jump systems (SSMJSs) with multiplicative noise. The parametric uncertainties here are allowed to be norm-bounded. The asynchronous phenomenon between original modes and controller modes leads to the resultant closed-loop system constructing a hidden Markov model (HMM). A convinced and detailed proof for the first time is proposed to ensure nominal SSMJSs with multiplicative noise and completely known information to be stochastically admissible with a prescribed H_∞ performance. To conquer the nonlinear difficulties incurred by the coupling of Lyapunov variables and controller gains, several effective strategies such as the matrix augmentation, special decomposition and introduction of auxiliary matrices are used. Furthermore, even in the simultaneous presence of singularity, multiplicative noise, parametric uncertainties as well as partial observation information, an asynchronous output feedback controller is successfully designed such that the uncertain SSMJS with multiplicative noise is stochastically admissible while achieving the required H_∞ performance. Finally, numerical examples are presented to demonstrate the effectiveness of proposed results.

本文专用于异步ħ _∞一类的离散时间不确定奇异随机马尔可夫跳变系统的（SSMJSs）与乘法噪声输出反馈控制。此处的参数不确定性可以规范。原始模式和控制器模式之间的异步现象导致最终的闭环系统构造了隐马尔可夫模型（HMM）。首次甲确信和详细的证明提出，以确保与乘性噪声和完全已知信息标称SSMJSs为与规定的随机受理ħ _∞性能。为了克服由Lyapunov变量和控制器增益耦合引起的非线性困难，使用了几种有效的策略，例如矩阵扩充，特殊分解和辅助矩阵的引入。此外，即使在奇点，乘性噪声的同时存在，参数不确定性以及部分观察信息，异步输出反馈控制器被成功地设计使得与乘性噪声的不确定SSMJS是随机受理，同时实现所需的ħ _∞性能。最后，通过数值例子说明了所提出结果的有效性。