Title :
H∞ filtering of 2-D discrete systems
Author :
Du, Chunling ; Xie, Lihua ; Soh, Yeng Chai
Author_Institution :
Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore
fDate :
6/1/2000 12:00:00 AM
Abstract :
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
Keywords :
H∞ optimisation; discrete systems; filtering theory; matrix algebra; 1D systems; 2D bounded real lemma; 2D discrete systems; 2D local state-space model; Fornasini-Marchesini second model; Riccati difference equation; Riccati inequality; finite horizon H∞ filtering; infinite horizon H∞ filtering; linear discrete systems; linear matrix inequality; state-space solution; Difference equations; Estimation error; Filtering algorithms; Infinite horizon; Kalman filters; Linear matrix inequalities; Nonlinear filters; Power system modeling; Riccati equations; Two dimensional displays;
Journal_Title :
Signal Processing, IEEE Transactions on
