H<inf>∞</inf> finite-horizon filtering for discrete piecewise linear systems with infinite distributed delays and quantization effect

Abstract

This paper deals with the H ∞ finite-horizon filtering for discrete piecewise linear systems with infinite distributed delays and quantization effect. The modes and their transitions of augmented piecewise linear systems are formulated. The quantisation phenomenon is described by the logarithmic function and the time delays are assumed to be randomly occurred and infinitely distributed in the discrete-time domain. Attention in this paper is focused on the design of a H ∞ filter such that, for the quantisation phenomenon and randomly occurred time delays, the H ∞ performance of the augmented dynamic system is guaranteed with a prescribed attenuation level γ. Such a technique relies on the forward solution to a set of recursive linear matrix inequalities. It is worth mentioning that, in the filtering process, the information of both the current measurement and the previous state estimate is employed to estimate the current state. Finally, a simulation example is exploited to show the effectiveness of the method proposed in this paper.