In this study, we concentrate on the problem of a finite-time reliable filter design for discrete-time Takagi–Sugeno fuzzy semi-Markovian jump systems with time-varying delay, sensor faults and randomly occurring uncertainties. To be precise, the time-varying transition probability matrices for the considered system are described by a semi-Markov process. Specifically, the objective is to design a reliable filter ensuring the strict dissipativity performance of the augmented filtering error system in the presence of sensor failures. Further, the stochastic variables describing the random nature of the parameter uncertainties are assumed to follow the Bernoulli distribution. A new finite-time stochastic stability criterion based on reciprocally convex approach and Lyapunov–Krasovskii stability theory is established in terms of linear matrix inequalities for the considered Takagi–Sugeno fuzzy semi-Markovian jump systems. Moreover, the delay-dependent conditions are established to guarantee the augmented filtering error system to be stochastically finite-time bounded and to achieve a prescribed strict dissipativity performance level for all admissible uncertainties and sensor faults. Finally, a numerical example is provided to show the correctness and effectiveness of the proposed method.

在这项研究中，我们专注于具有时变时滞，传感器故障和随机发生的不确定性的离散时间Takagi-Sugeno模糊半马尔可夫跳跃系统的有限时间可靠滤波器设计问题。准确地说，所考虑系统的时变转移概率矩阵是通过半马尔可夫过程描述的。具体而言，目的是设计一种可靠的滤波器，以确保在出现传感器故障的情况下，增强的滤波误差系统具有严格的耗散性能。此外，假设描述参数不确定性的随机性的随机变量遵循伯努利分布。针对考虑的Takagi-Sugeno模糊半马尔可夫跳跃系统，基于线性矩阵不等式，建立了基于倒凸方法和Lyapunov-Krasovskii稳定性理论的新的有限时间随机稳定性准则。此外，建立了与延迟有关的条件，以确保增强的滤波误差系统受到随机有限时限的限制，并针对所有可容许的不确定性和传感器故障，达到规定的严格耗散性能水平。最后，通过算例说明了该方法的正确性和有效性。建立与延迟有关的条件，以确保增强的滤波误差系统受到随机时限限制，并针对所有可容许的不确定性和传感器故障，达到规定的严格耗散性能水平。最后，通过算例说明了该方法的正确性和有效性。建立与延迟有关的条件，以确保增强的滤波误差系统受到随机时限限制，并针对所有可容许的不确定性和传感器故障，达到规定的严格耗散性能水平。最后，通过算例说明了该方法的正确性和有效性。