Robust filtering for 2-D discrete-time linear systems with convex-bounded parameter uncertainty

This paper is concerned with the problems of robust H∞H∞ and H2H2 filtering for 2-dimensional (2-D) discrete-time linear systems described by a Fornasini–Marchesini second model with matrices that depend affinely on convex-bounded uncertain parameters. By a suitable transformation, the system is represented by an equivalent difference-algebraic representation. A parameter-dependent Lyapunov function approach is then proposed for the design of 2-D stationary discrete-time linear filters that ensure either a prescribed H∞H∞ performance or H2H2 performance for all admissible uncertain parameters. The filter designs are given in terms of linear matrix inequalities. Numerical examples illustrate the effectiveness of the proposed filter design methods.