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The aim of this study is to address the challenge of H∞ filtering for 2-D systems with time delays. We will employ the well-known Fornasini-Marchesini state model with delay to mathematically describe these 2-D systems. Our objective is to develop a full-order filter that not only ensures the asymptotic stability of the expanded system but also maintains H∞ performance. Our approach will rely on Linear Matrix Inequalities (LMIs) to establish the conditions for the filter’s existence and convert the filter design problem into a convex optimization problem. Finally, we conclude with an illustrative example to demonstrate the effectiveness of the proposed filter design.

The purpose of this paper is to address the problem of assessing the stability of singular time-varying delay systems. In order to highlight the relations between the delay and the state, the singular system is transformed into a neutral form. Then, a model transformation using a three-terms approximation of the delayed state is exploited. Based on the lifting method and the Lyapunov–Krasovskii functional (LKF) method, a new linear matrix inequality (LMI) is obtained, allowing conclusions on stability to be drawn using the scaled small gain theorem (SSG). The use of SSG theorem for stability of singular systems with time-varying delay has not been investigated elsewhere in the literature. This represents the main novelty of this article. The result is applicable for assessing the stability of both singular systems and neutral systems with time-varying delays. The less conservativeness of the stability test is illustrated by comparison with recent literature results. [ABSTRACT FROM AUTHOR]

This paper investigates the $$H_{\infty }$$ control problem for two-dimensional (2D) Takagi-Sugeno (T-S) fuzzy systems in a Fornasini-Marchesini second (FM II) model with stochastic perturbation. Our aim is to develop the state feedback control for 2D (T-S) fuzzy systems with stochastic perturbation and reduce the conservatism by using some slack matrices. Attention is focused on the design of the state feedback control, which guarantees the closed-loop system to be mean-square asymptotically stable and to have a prescribed $$H_{\infty }$$ performance. Sufficient conditions are derived for the existence of such controls in terms of linear matrix inequalities, and the corresponding control synthesis problem, then, is solved. Numerical examples are given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The H filtering problem for two-dimensional Takagi-Sugeno fuzzy systems described by the Fornasini-Marchesini (FM) model is studied. Attention is focused on the design of an H fuzzy filter such that the filter error system is asymptotically stable and preserves a guaranteed H performance. By using basis-dependent Lyapunov functions and adding slack matrix variables, the coupling between the Lyapunov matrix and the system matrices is eliminated. Then, a linear matrix inequality (LMI)-based approach is developed for designing the H fuzzy filter. Finally, an illustrative example is provided to show the effectiveness of the proposed approach and less conservatism. [ABSTRACT FROM AUTHOR]