Model reduction for two-dimensional systems with generalized H∞ approximation performance

The paper investigates generalized H_∞ model reduction for two-dimensional (2-D) systems represented by the Roesser model and the Fornasini-Machesini local state-space model, respectively. The generalized H_∞ norm of 2-D systems is introduced to evaluate the approximation error over a specific finite frequency (FF) domain. In light of the 2-D generalized Kalman-Yakubovich-Popov lemmas, sufficient conditions in terms of linear matrix inequalities are derived for the existence of a stable reduced-order model satisfying a specified generalized H_∞ level. Several examples are provided to illustrate the effectiveness and advantages of the proposed method. Compared with most of the existing results, the proposed method has the following merits: 1) Both important types of 2-D models are considered in a unified framework, and no structural assumption is made for the plant model. 2) An upper bound on the generalized H_∞ error can be obtained, and no weighting function is needed. 3) The proposed method is applicable to multiple FF specifications.