Two-Dimensional Hankel Norm Performance of Roesser-Type Filters

This article introduces a novel approach to examining the unfavorable memory effects of two-dimensional (2-D) Roesser-type filters based on the 2-D Hankel norm performance. Novel analysis criteria are obtained such that the 2-D Roessertype filters associated with saturation have the guaranteed 2-D Hankel norm performance bound. These criteria can analyze the undesired effect reduction of Roesser-type filters for past horizontal and vertical excitations. Without external horizontal and vertical input signals, the 2-D asymptotic convergence of Roesser-type filters is ascertained under the proposed novel criteria. Finally, a numerical demonstration is given to verify the validity of the obtained criteria. The criteria presented in this paper for 2-D filters and those reported in our recent paper for one-dimensional (1-D) filters can provide a whole analysis framework for the undesired memory effects of filters.