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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]

Summary: This paper investigates the H∞ model reduction problem over finite frequency ranges for continuous time Takagi‐Sugeno (T‐S) fuzzy systems. Given an asymptotically stable system, our aim is to find a stable reduced‐order system in such a way that the error of the transfer function between the original system and the reduced‐order one is bounded over a finite frequency range. By using the Finsler's lemma, new sufficient conditions in terms of linear matrix inequalities are derived in different frequency ranges. These conditions provide extra degrees of freedom in the optimization of the H∞ performance when the frequency range of noises is known beforehand. Finally, we demonstrate via numerical examples that our method can achieve much smaller approximation error than existing approaches. [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]

This paper deals with $$H_{\infty }$$ filtering problem of linear discrete-time uncertain systems with finite frequency input signals. The uncertain parameters are supposed to reside in a polytope. By applying the generalized Kalman-Yakubovich-Popov lemma, polynomially parameter-dependent Lyapunov function and some key matrices to eliminate the product terms between the filter parameters and the Lyapunov matrices, an improved condition is obtained for analyzing the $$H_{\infty }$$ performance of the filtering error system. Then sufficient condition in terms of linear matrix inequality is established for designing filters with a guaranteed $$H_{\infty }$$ filtering performance level. Finally, a numerical examples are used to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The problem of $$H_{\infty }$$ filter design for a class of 2D systems is solved here in the presence of intermittent measurements. Data dropouts are characterized using a stochastic variable satisfying the Bernoulli random binary distribution. Our attention is focused on the design of reduced-order $$H_{\infty }$$ filters such that the filtering error 2D stochastic system is robust mean-square asymptotically stable and fulfills a given $$H_{\infty }$$ disturbance attenuation level. We use a new formulation for a class of 2D system Fornasini-Marchesini (FM) models. A sufficient condition is established by means of the linear matrix inequalities (LMI) technique. The efficiency and viability of the proposed techniques and tools are demonstrated through a set of numerical examples. [ABSTRACT FROM AUTHOR]

This paper tackles the $$H_{\infty }$$ filtering problem for 2-D discrete systems. The approach is based on the Roesser model. The objective is to propose a new design with sufficient condition via LMI formulations. Less conservative results are obtained by introducing additional free parameters by using the Finsler's Lemma. This method provides extra degree of freedom in optimization of the $$H_{\infty }$$ performance. The efficiency of the proposed approach is shown by several examples. [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]