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The problem of input–output stability analysis and stabilisation of discrete Takagi–Sugeno (T–S) fuzzy systems with a time-varying delay via an input–output (I–O) approach is investigated in this paper. Using a three-term approximation-based model, a forward subsystem with three constant delays and a feedback subsystem are presented. Two separate input–output stability criteria have been formulated, using an input–output approach and a scaled small gain theorem: a criterion based on the lifting method, a non-quadratic Lyapunov function, and bounded real lemma, another criterion based on a non-quadratic Lyapunov–krasovskii functional approach. Using this result, the input–output stabilisation problem is resolved through the so-called parallel distributed compensation (PDC) scheme. The conditions obtained are presented in terms of linear matrix inequalities (LMIs). Three numerical examples are provided to demonstrate the advantages and merit of the proposed method. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of delay-dependent robust filtering design for polytopic systems with a time-varying delay. A new model transformation is firstly applied by employing a three-term approximation for the delayed state, which leads to a smaller approximation error than the two-term approximation. Then, based on the scaled small-gain Theorem combined with an appropriate Lyapunov-Krasovskii Functional, the performance analysis of the filtering error system is examined and then the full- and reduced-order filters are designed in terms of linear matrix inequalities via a simple linearisation technique. Before the end, a sufficient condition is presented to solve the problem of filtering design for a time-delay system without polytopic uncertainties. Finally, illustrative examples are presented to demonstrate the validity of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of the filtering for discrete-time Takagi-Sugeno fuzzy stochastic systems. The objective is to find new filter design conditions ensuring both the mean square asymptotic stability and prescribed performance of the filtering error system. By means of a fuzzy Lypunov function and by introducing some slack variables through an appropriate use of the projection lemma, new analysis conditions of performance are proposed. Then, the full and reduced-order filter design conditions are proposed in Linear Matrix Inequality form. Finally, to illustrate the proposed approach, simulation and comparison with existing results in the literature are given. [ABSTRACT FROM AUTHOR]

This paper investigates the design problem of robustH∞filtering for uncertain two-dimensional (2D) continuous systems described by Roesser model with polytopic uncertainties and frequency domain specifications. Our aim is to design a new filter guaranteeing anH∞performance level in specific finite frequency (FF) domains. Using the well-known generalised Kalman Yakubovich Popov lemma and homogeneous polynomially parameter-dependent matrices of arbitrary degrees, sufficient conditions for the existence ofH∞filters for different FF ranges are proposed and then unified in terms of solving a set of linear matrix inequalities. Illustrative examples are provided to show the usefulness and potential of the proposed results. [ABSTRACT FROM PUBLISHER]

The resilient sliding mode control (SMC) problem for a class of discrete-time descriptor Takagi–Sugeno (T-S) fuzzy systems with multiple state delays is addressed. Attention is focused on the design of a discrete-time SMC such that the admissibility as well as theH∞ performance requirement of the sliding mode dynamics can be guaranteed in the presence of time delays and external disturbances. Based on a new sliding function, a delay-dependent sufficient condition is established to ensure the desired performance of the sliding mode dynamics on the specified sliding mode surface. Moreover, a resilient SMC law is established to satisfy the reaching condition. Finally, two examples are given to show the effectiveness and advantages of the proposed design SMC scheme. [ABSTRACT FROM AUTHOR]