H∞ deconvolution filtering of 2-d digital systems

Abstract

This paper deals with the problem of two-dimensional (2-D) digital system deconvolution under the performance specification. The 2-D digital system under consideration is expressed by the Fornasini-Marchesini local state-space (FM LSS) model. For a given 2-D digital system, a 2-D deconvolution filter is designed to reconstruct the 2-D signal to meet a prescribed performance specification. A key analytical means for the deconvolution filter design is the 2-D bounded realness property derived in this paper. Applying this property, the 2-D deconvolution filter design is formulated into a convex optimization problem characterized by linear matrix inequalities (LMIs). A procedure for the design of an deconvolution filter for a given 2-D digital system with measurement noise is developed first. The LMI approach to the 2-D deconvolution filtering problem is further extended to the 2-D robust deconvolution filtering problem with polytopic modeling uncertainties in the 2-D system. The obtained results on the 2-D deconvolution filtering and robust deconvolution filtering problems are demonstrated with examples.

H∞ filtering for continuous fractional‐order 2D Roesser model: The 0<α≤1 case

“…The $$$ {H}_{\infty } $$$ filtering problem of 2D continuous‐discrete Roesser systems with state‐delay in finite frequency domains is solved in Wang et al [19]. The bounded real lemmas and the $$$ {H}_{\infty } $$$ deconvolution filter design for the 2D digital system are derived in LMI form in Xie et al [20]. The bounded real lemmas for 2D singular Roesser models are investigated in terms of LMIs, and the $$$ {H}_{\infty } $$$ model reduction problem is solved in Xu et al [21].…”

A Survey on the Stability of 2-D Discrete Systems Described by Fornasini-Marchesini Second Model

“…Hence, H  filtering tends to be more robust when there exist additional parameter disturbances in models and it is very appropriate in a number of practical situations [41]. The 2-D filtering approach with H  performance measure has been developed in [41][42][43][44][45][46][47].…”