H∞ state estimation of 2D discrete systems

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