H Filtering of 2-D Discrete Systems Described by FM LSS Model

Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 278)


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.


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© Springer-Verlag Berlin Heidelberg 2002

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