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Abstract This paper investigates the β -dissipativity-based reliable non-fragile sampled-data control problem for a class of interval type-2 (IT2) fuzzy systems. In particular, it is allowed to have randomly occurring time-varying delays in the controller design, which are modeled by Bernoulli distributed white noise sequences. Precisely, the IT2 fuzzy model and the non-fragile sampled-data controller are formulated by considering the mismatched membership functions. By constructing an appropriate Lyapunov–Krasovskii functional, a set of delay-dependent conditions is derived to guarantee that the closed-loop IT2 fuzzy system is strictly < Q,S,R > - β -dissipative. Moreover, the gain matrices of feedback reliable non-fragile sampled-data controller are derived in terms of linear matrix inequalities (LMIs), which can be solved by using existing LMI solvers. Two numerical examples are eventually given to illustrate the applicability and effectiveness of the proposed controller design technique. Highlights • An interval type 2 fuzzy model is formulated with upper and lower membership functions such that it can capture the uncertainties subject to probabilistic delay, actuator faults and gain fluctuations in the control design. • A generalized actuator fault model containing both linear and nonlinear terms is implemented in the non-fragile sampled-data controller design and the proposed controller precisely deals with the gain fluctuations. • By constructing an appropriate Lyapunov–Krasovskii functional together with Wirtinger-based double integral inequality, a new set of sufficient criteria is developed for obtaining the required result. • The obtained results are verified through numerical examples, which reveal that the proposed method yields less conservative results and better performance for the considered interval type 2 fuzzy model. [ABSTRACT FROM AUTHOR]

Abstract: The problem of reliable sampled‐data control design for uncertain singular fuzzy system with randomly occurring delay and nonlinear actuator failures is studied in this paper. The fault model is composed of two parts in which, linear part stands for the gain missing of actuators that vary with the true control input linearly, while the nonlinear part indicates some bounded nonlinear variation. Moreover, the time delay which encountering in the proposed controller is assumed to be randomly varying and satisfies Bernoulli distributed probabilities. By constructing a proper time‐dependent Lyapunov functional, some novel sufficient conditions are derived in terms of linear matrix inequalities (LMIs) for the existence of robustly stochastically stabilizing reliable sampled‐data controllers. Two simulation examples are given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the finite-time mixedH∞and passivity performance analysis and filter design for a class of uncertain nonlinear discrete-time Markovian jump systems (MJSs) described by Takagi–Sugeno fuzzy model with nonhomogeneous jump processes. In this paper, the proposed MJSs fuzzy model is formulated with norm-bounded parameter uncertainties and time-varying jump transition probability matrices. In particular, the time-varying transition probability matrices are expressed in respect of a polytope. By constructing a suitable Lyapunov functional, a new set of sufficient conditions is derived in the form of linear matrix inequalities (LMIs) to ensure that the filtering error system is robustly stochastically finite-time bounded and a prescribed mixedH∞and passive performance index is achieved. Moreover, the robust mixedH∞and passivity filter design gain matrices can be computed from the obtained LMIs. Furthermore, the developed results unifyH∞and passive filtering problems in a single framework. Finally, two numerical examples including an application-oriented example are provided to demonstrate the effectiveness of the proposed filter design technique. [ABSTRACT FROM PUBLISHER]

Abstract In this paper, we consider the reliable non-fragile H ∞ control design problem for a class of discrete-time interval-valued fuzzy systems with actuator faults. More precisely, the actuator fault model considered in the controller design consists of linear and nonlinear fault terms. The main focus of this paper is to design a non-fragile state feedback controller that is characterized by membership functions described by upper and lower membership functions and nonlinear weighting functions. It should be mentioned that the proposed interval-valued fuzzy system and the controller do not share same membership functions. A novel set of sufficient conditions is obtained by transforming the controller design problem into a multi-objective convex optimization problem based on the linear matrix inequality and the Lyapunov functional approaches, which ensures the robust asymptotic stability of the addressed system with a desired H ∞ performance index. Finally, two numerical examples, including an application-oriented model, mass-spring-damping system are presented to demonstrate the effectiveness of the proposed design technique. [ABSTRACT FROM AUTHOR]