H∞ filtering for a class of 2-D discrete-time parameter-varying systems

This paper deals with H_∞ filtering for two-dimensional (2-D) discrete-time linear parameter-varying systems described by the Fornasini-Marchesini second model with matrices that depend rationally on convex-bounded time-varying parameters. A method is proposed for the design of robust 2-D filters with a prescribed H_∞ performance for all admissible parameters´ trajectories. The filter design method builds on a difference-algebraic representation of the underlying system and is based on a parameter-dependent Lyapunov function with affine dependence on the system parameters. The filtering method is then adapted for designing gain-scheduled (parameter-varying) H_∞ filters. The proposed filter designs are tailored via linear matrix inequalities. A numerical example illustrates the potentials of the filtering methods.