Robust H∞ Filtering for 2-D Discrete-Time Linear Systems with Convex-Bounded Parameter Uncertainty

This paper is concerned with the robust H∞ filtering problem for 2-dimensional (2-D) discrete-time linear systems described by a Fornasini-Marchesini second model with convex-bounded parameter uncertainty. By a suitable transformation, the system is converted into an equivalent difference-algebraic representation. A parameter-dependent Lyapunov function approach is then proposed for the design of a 2-D stationary discrete-time linear filter that ensures a prescribed upper-bound on the H∞-norm of the transfer function of the estimation error system for all admissible uncertain parameters. The filter design is given in terms of linear matrix inequalities.