H ∞ Fuzzy filtering for nonlinear singular systems with time-varying delay

Huan Liu ,Ding Zhai,Qingling Zhang,An-Yang Lu

doi:10.1186/s13662-015-0427-5

Abstract

This paper considers the $H_{\infty}$ fuzzy filtering problem for continuous-time nonlinear singular systems with time-varying delay through the T-S fuzzy model approach. Firstly, by combining a reciprocally convex combination lemma and the fuzzy Lyapunov-Krasovskii function method, a new bounded real lemma (BRL) is proposed such that the resultant closed-loop systems are admissible and satisfy the prescribed $H_{\infty}$ disturbance attenuation. Then, by using the matrix decoupling technique, we translate the BRL into another form, which separates the coefficient matrices of systems and Lyapunov matrices. On the basis of such a new form of BRL, the fuzzy filter design problem is solved by checking the feasibility of a series of linear matrix inequalities (LMIs), and the filter gains can also be provided explicitly. Numerical examples are presented to show the reduction of the conservativeness compared to some published results in the literature.

Highlights

Nowadays, various approaches have been proposed for the filter design, such as Kalman filter design [, ], H∞ filter design [ – ] and so on
Based on a fuzzy Lyapunov-Krasovskii functional (LKF), and by virtue of a reciprocally convex combination lemma, a new bounded real lemma (BRL) is presented for the nonlinear singular delayed systems, and another form of such BRL is derived by using the matrix decoupling technique
3 Main results initially, we present a novel bounded real lemma for fuzzy singular system ( ) with time-varying delay ( ), which focuses on tackling the time-varying delay by virtue of the reciprocally convex combination method and fuzzy Lyapunov-Krasovskii function method, another form of the proposed bounded real lemma is derived by using the matrix decoupling technique

Summary

Introduction

Various approaches have been proposed for the filter design, such as Kalman filter design [ , ], H∞ filter design [ – ] and so on. By using the T-S fuzzy model approach, [ ] considered the H∞ filter design for nonlinear systems with time-varying delay where the free-weighting matrix method and matrix decoupling method are utilized. Based on a fuzzy Lyapunov-Krasovskii functional (LKF), and by virtue of a reciprocally convex combination lemma, a new BRL is presented for the nonlinear singular delayed systems, and another form of such BRL is derived by using the matrix decoupling technique. The filter design problem to be addressed here can be formulated as follows: for the fuzzy singular system ( ) with time-varying delay ( ) and a prescribed H∞ bound γ > , design a filter in the form of ( ) such that the filter error system ( ) with w(t) = is admissible and under the zero initial condition.

Bounded real lemma

Conclusion