This paper concentrates on analyzing the stability problem for fuzzy Markov jump systems (FMJSs) via stochastic sampling and $H_{\infty }$-based sampled-data control scheme. With the help of input-delay technique, the probabilistic sampling intervals are reconstructed into a continuous time-varying system under stochastic parameters in the system matrices. Subsequently, a set of sufficient conditions ensuring the stochastic stability of the addressed FMJS with an allowable $H_{\infty }$ disturbance attenuation value is formulated in the form of linear matrix inequalities (LMIs) by choosing a proper Lyapunov–Krasovskii functional involving triple integral terms and utilizing Wirtinger-based integral inequality. The desired sampled-data control gain can be determined in terms of the solution to the obtained LMIs. Lastly, the developed theoretical results and the benefits of the desired controllers are verified through numerical examples including a single link robot arm system.

本文主要通过随机抽样和模糊分析来分析模糊马尔可夫跳跃系统（FMJSs）的稳定性问题。 $H_{\infty }$的采样数据控制方案。借助输入延迟技术，将概率采样间隔重构为系统矩阵中随机参数下的连续时变系统。随后，一组充分的条件确保了所寻址的FMJS的随机稳定性以及可允许的范围。$H_{\infty }$通过选择适当的涉及三重积分项的Lyapunov-Krasovskii泛函并利用基于Wirtinger的积分不等式，以线性矩阵不等式（LMI）的形式表示干扰衰减值。可以根据对获得的LMI的解来确定所需的采样数据控制增益。最后，通过包括单连杆机器人手臂系统在内的数值示例，验证了所开发的理论结果和所需控制器的优势。