*H*_{∞} Filtering of 2-D Discrete Systems Described by FM LSS Model

## Abstract

In this chapter, we develop a 2-D filtering approach with an *H* _{∞} performance measure for 2-D discrete systems described by the 2-D FM LSS model [28]. We consider both the finite horizon and infinite horizon filtering problems. Based on the 2-D Bounded Real Lemma developed in Chapter 2, we first study the finite horizon *H* _{∞} filtering problem. It is shown that the finite horizon *H* _{∞} filtering problem is solvable if a 2-D Riccati difference equation admits a positive definite solution. The result extends the well known 1-D *H* _{∞} filtering result to the 2-D case. Furthermore, we shall develop both a Riccati inequality approach and an LMI approach to the infinite horizon *H* _{∞} filtering problem. Two examples will be given to illustrate the applications of the results. The first one is on a stationary random field in image processing and the other on a 2-D digital filter.

## Preview

Unable to display preview. Download preview PDF.