Filtering of discrete linear repetitive processes with ℋ _∞ and ℓ₂-ℓ_∞ performance

This paper considers the general filtering problem for a distinct class of two-dimensional (2-D) discrete linear systems, i.e. information propagation in two independent directions, known as discrete linear repetitive processes which are of both system-theoretic and applications interest. In particular, new results on the design of filters with guaranteed levels of performance are developed. These take the form of algorithms for the design of an ℋ_∞ and ℓ₂-ℓ_∞ dynamic output feedback filter which guarantees that the resulting filtering error process is stable and has prescribed disturbance attenuation performance as measured by ℋ_∞ and ℓ₂- ℓ_∞ norms.