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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]

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]