A Semi-Markovian Model Approach to Resilient Fault-Tolerant Control of Interval Type-2 Fuzzy Systems With Stochastic Actuator Failures and Its Applications

Abstract

This article mainly presents a fresh systematic framework to tackle the resilient fault-tolerant sampled-data control (SDC) synthesis problem for networked interval type-2 fuzzy systems (IT-2FSs) suffering with semi-Markovian-type jump actuator failures (SMJAFs) and mismatched membership functions (MMFs), which portrays more features than some prior developments. The principally target of the addressed problem under this systematic investigation is to precisely architect a faulty mode-dependent sampled-data controller such that the resultant IT-2FSs are asymptotically stable with a prescribed $H_{\infty }$ attenuation level simultaneously. Firstly, in a departure from conventional control approaches, to better depict the stochastic actuator failures (SAFs) and cater to the engineering practice more accurately, a neoteric control input model that incorporated with semi-Markovian jump-type faulty coefficients with stochastically occurring bias terms is reconstructed for IT-2FSs in specifically. Secondly, the occurrence of controller gain fluctuations is randomly, which is regulated by a Bernoulli random binary distribution with a pre-known probability distribution. Thirdly, in comparison with majority of the existing SDC strategies, the intrinsic lag signal $\varrho$ is intensionally introduced in the control loop, which exploited initially to handle the IT-2 fuzzy control synthesis issue. In doing so, a novelty looped-type semi-Markovian Lyapunov functional alleged dual-sided looped semi-Markovian Lyapunov functional that adequate acquisition the characteristic information of whole sampling intervals from $x\left(t_k\right)$ to $x\left(t\right)$ and $x\left(t\right)$ to $x\left(t_{k+1}\right)$ along with $x(t_k-\varrho )$ to $x(t-\varrho )$ and $x(t-\varrho )$ to $x(t_{k+1}-\varrho )$ is innovatively reconstructed. Subsequently, with the aid of the structured Lyapunov functional and stochastic analysis technique, sufficient conditions are ultimately formulated in the configuration of a cluster of parameterized linear matrix inequalities (PLMIs) such that the resultant IT-2FSs can achieve asymptotically stable. More specifically, some adjunctive matrices $\left[{\yen }_{ij,m}^{\left(𝒥\right)}\right({𝒯}_k\left)\right](𝒥=1,2)$ are designedly exhibited to further loose the strict constraints, which caused by the asynchronous membership functions (AMFs). Conclusively, the potency and accuracy of the developed control synthesis framework are discussed and simulations on three practical applications for further demonstrations.