This paper focuses on the problem of designing H∞ filters for nonlinear systems with time-varying delay via Takagi-Sugeno (T-S) fuzzy models. Some new results on H∞ filter design are proposed by estimating the upper bounds of the derivatives of Lyapunov functionals without ignoring some useful terms, which improve the existing ones. In addition, a sufficient condition for the existence of such an H∞ filter is established in terms of solutions to a set of linear matrix inequalities (LMIs). Finally, two examples are given to demonstrate the effectiveness of the proposed method.

New Results on $H_\infty$ Filter Design for Nonlinear Systems With Time Delay via T–S Fuzzy Models

This paper focuses on the fuzzy-H∞-filter-design problem for Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delays. Two cases of the time-varying delays are considered: 1) The delays are differentiable and have both the lower and upper bounds of the delay derivatives, and 2) the delays are bounded but not necessary to be differentiable. Since we employ a new fuzzy Lyapunov-Krasovskii functional (LKF) and estimate a tighter upper bound of its derivative, the proposed delay-derivative-dependent bound-real-lemma (BRL) condition has advantages over some previous results in that it enlarges the application scope but has less conservatism, which is established theoretically. The BRL condition that depends on both the upper and lower bounds of the delay derivatives is derived. Then, based on the aforesaid BRL, a new fuzzy H∞ filter scheme is proposed, and a sufficient condition for the existence of such a filter is established in terms of linear-matrix inequalities (LMIs). Finally, some numerical examples and an application to the truck-trailer system are utilized to demonstrate the effectiveness and reduced conservatism of our results.

New Results on a Delay-Derivative-Dependent Fuzzy H $^\infty$ Filter Design for T–S Fuzzy Systems

Non-fragile H filtering for delayed TakagiSugeno fuzzy systems with randomly occurring gain variations

This paper proposes a novel H∞ filtering technique for a class of discrete-time fuzzy systems. First, a novel kind of fuzzy H∞ filter, which is homogenous polynomially parameter dependent on membership functions with an arbitrary degree, is developed to guarantee the asymptotic stability and a prescribed H∞ performance of the filtering error system. Second, relaxed conditions for H∞ performance analysis are proposed by using a new fuzzy Lyapunov function and the Finsler lemma with homogenous polynomial matrix Lagrange multipliers. Then, based on a new kind of slack variable technique, relaxed linear matrix inequality-based H∞ filtering conditions are proposed. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approach.

Homogenous Polynomially Parameter-Dependent $H_{ \infty}$ Filter Designs of Discrete-Time Fuzzy Systems

This paper investigates the robust filtering problem for a class of nonlinear systems described by affine fuzzy parts with norm-bounded uncertainties. The system outputs are chosen as the premise variables of fuzzy models, and their measured values are chosen as the premise variables and inputs of fuzzy filters. The measurement errors between the outputs of the plant and the inputs of the filter are considered, and as a result, the plant and the estimator cannot always evolve in the same region at the same time, especially in the neighborhoods of region boundaries. By using a piecewise Lyapunov function combined with S-procedure and adding slack matrix variables, a fuzzy-basis-dependent mixed $l_{1}/H_{\infty}$ filter design method is obtained in the formulation of linear matrix inequalities, which allows for reducing the worst case peak output due to the measurement errors, and satisfying an $H_{\infty}$ -norm constraint. In contrast to existing work, the proposed fuzzy-basis-dependent filter can guarantee a better $H_{\infty}$ performance and less computational burden. Finally, a numerical example illustrates the effectiveness of the proposed method.

Robust Mixed $l_{1}/H_{\infty}$ Filtering for Affine Fuzzy Systems With Measurement Errors

A new fuzzy H∞ filter design for nonlinear continuous-time dynamic systems with time-varying delays

This paper focuses on the problem of H ∞ filter design for nonlinear systems with time-varying delays. A new approach of filter design is proposed. The present results may improve the existing ones due to a method to estimate the upper bound of the derivative of Lyapunov functional without ignoring some useful terms. A sufficient condition for the existence of such a filter is established by using the linear matrix inequality (LMI) approach. Finally, an example is given to demonstrate the effectiveness and the benefits of the proposed method.

Yakun Su

Papers

A new fuzzy H∞ filter design for nonlinear continuous-time dynamic systems with time-varying delays

Delay-dependent H ∞ filtering for nonlinear systems via T-S fuzzy model approach