H∞ filtering of 2-D discrete systems

This paper deals with H_∞ filtering of two-dimensional (2-D) linear discrete systems described by a 2-D local state-space (LSS) Fornasini-Marchesini (1978) second model. Several versions of the bounded real lemma of the 2-D discrete systems are established. The 2-D bounded real lemma allows us to solve the finite horizon and infinite horizon H_∞ filtering problems using a Riccati difference equation or a Riccati inequality approach. Further a solution to the infinite horizon H_∞ filtering problem based on a linear matrix inequality (LMI) approach is developed. Our results extend existing work for one-dimensional (1-D) systems to the 2-D case and give a state-space solution to the bounded realness of 2-D discrete systems as well as 2-D H_∞ filtering for the first time. Numerical examples are given to demonstrate the Riccati difference equation approach to the 2-D finite horizon H_∞ filtering problem and the LMI approach to the 2-D infinite horizon H_∞ filtering problem