H∞ and Robust Control of 2-D Systems in FM Second Model
Multidimensional Systems and Signal Processing
Stability and Stabilization of Uncertain 2-D Discrete Systems with Stochastic Perturbation
Multidimensional Systems and Signal Processing
Filtering for uncertain 2-D discrete systems with state delays
Signal Processing
Robust stability and robust H∞ control of 2-D discrete systems with polytopic uncertainty
Math'04 Proceedings of the 5th WSEAS International Conference on Applied Mathematics
H∞ filtering of 2-D discrete state-delayed systems
Multidimensional Systems and Signal Processing
Robust guaranteed cost control for a class of two-dimensional discrete systems with shift-delays
Multidimensional Systems and Signal Processing
Robust filtering for 2-D discrete-time linear systems with convex-bounded parameter uncertainty
Automatica (Journal of IFAC)
$${{\mathcal H}_{\infty}}$$ control of linear multidimensional discrete systems
Multidimensional Systems and Signal Processing
Fuzzy modeling and H∞ control for general 2D nonlinear systems
Fuzzy Sets and Systems
Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions
Multidimensional Systems and Signal Processing
Multidimensional Systems and Signal Processing
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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