Robust H∞ filter design of uncertain descriptor systems with discrete and distributed delays

Dong Yue Dong Yue,Qing-Long Han Qing-Long Han

doi:10.1109/cdc.2003.1272631

Abstract

The robust H/sub /spl infin// filtering problem for a class of continuous-time uncertain linear descriptor systems with time-varying discrete and distributed delays is investigated. The time-delays are assumed to be constant and known. The uncertainties under consideration are norm-bounded, and possible time-varying, uncertainties. Sufficient condition for the existence of an H/sub /spl infin// filter is expressed in terms of strict linear matrix inequalities (LMIs). Instead of using decomposition technique, a unified form of LMIs is proposed to show the exponential stability of the augmented systems. The condition for assuring the stability of the fast subsystem is implied from the unified form of LMIs, which is shown to be less conservative than the characteristic equation based conditions or matrix norm based conditions. The suitable filter is derived through a convex optimization problem. A numerical example is given to show the effectiveness of the method.

Highlights

Signal estiination has received significant attention in the past decades
One of its main advantages is the fact that it is insensitive to the exact knowledge of the statistics of the noise signals
When there exist parameter uncertainties in the system’s model, robust H, filtering can provide a powerful signal estimation. It designs an asymptotically stable filter, based on an uncertain signal model, which ensures that the filtering error dynamics is asymptotically stable and that the &-induced gain from the noise signals to the filtering error remains bounded by a prescribed level for all allowed uncertainties

Summary

Introduction

Signal estiination has received significant attention in the past decades. Current efforts on this topic can be divided into two classes: namely Kalmk filtering approach and H , filtering approach.In the Kalman filtering approach, the system’s disturbances are assumed to be Gaussian noises with known statistics, see, for example, for linear systems [14], and for linear descriptor systems [l].When the system’s noise sources are assumed to be arbitrary signals with bounded energy (or average power), the H , filtering approach provides a guaranteed noise attention level. When there exist parameter uncertainties in the system’s model, robust H , filtering can provide a powerful signal estimation. In 1111, an H , filter design for precisely known systems with a single time delayed measurement was proposed.

Results

Conclusion