This paper addresses the observer-based finite-time \(H_{\infty }\) control problem for Takagi–Sugeno (T–S) fuzzy semi-Markovian jump systems with mode-dependent fast-varying delays, actuator faults, parameter uncertainties and partly uncertain transition rates. Firstly, a more general actuator fault model is considered and the fuzzy reliable observer-based control scheme is designed. By applying the new Lyapunov functional candidates, free-weighting matrix method and slack matrix variables, some negative integral terms can be adopted and the nonlinear terms caused by time delay and partly unknown transition rates can be dealt. Furthermore, novel sufficient conditions on guaranteeing the closed-loop system is stochastically finite-time bounded (SFTB) with the prescribed \(H_{\infty }\) level are proposed. Particularly, different from traditional slowly varying delays, the case of mode-dependent fast-varying delays which are more difficult to be dealt is considered in this paper. Lastly, a practical example is exploited to affirm the validity of the obtained results.

本文针对具有模式相关快变时滞，执行器故障，参数不确定性的Takagi–Sugeno（TS）模糊半马尔可夫跳跃系统，解决了基于观测器的有限时间\（H _ {\ infty} \）控制问题。部分不确定的过渡率。首先，考虑了更通用的执行器故障模型，并设计了基于模糊可靠观测器的控制方案。通过应用新的Lyapunov候选函数，自由加权矩阵方法和松弛矩阵变量，可以采用一些负积分项，并且可以解决由时间延迟和部分未知的跃迁率引起的非线性项。此外，具有规定的\（H _ {\ infty} \）的随机有限时限（SFTB）是保证闭环系统的新颖充分条件。级别的建议。特别是，与传统的缓慢变化的延迟不同，本文考虑了较难处理的模式相关的快速变化延迟的情况。最后，通过一个实例验证了所得结果的正确性。