Discussion on: 'Energy-to-Peak Model Reduction for 2-D Discrete Systems in Fornasini-Marchesini Form'

摘要

This paper considers the model reduction problem of 2-D discrete-time dynamical systems. Particularly, the authors focus on Fornasini-Marchesini (FM) second models (cf. [3,4]) as the representative mathematical models due to the fact that they include Rosser models (cf. [9]), Attasi models (cf.[l]) and FM first models (cf. [2]) as specialized forms. As the main results of this paper, the authors first provide a suffficient condition for 2-D FM second model to be asymptotically stable together with the rectriction that the L_∞ norm is less than a prescribed real number. And then, by using this sufficient condition, the authors also provide linear matrix inequality conditions for the dimension of the state space of a given 2-D FM second model to be reduced with respect to L_∞ norm criterion and the algorithm of the proposed model reduction. All of the above conditions obtained by the authors take the form of linear matrix inequalities so as to enable one to check the stability and the model reductionability of 2-D FM models with numerical computations which are familiar with the systems and control engineers. Thus, the results of this paper is useful for the sake of the model reduction of 2-D discrete-time systems and hence it is also a nice contribution as the mathematical tools for synthesis and analysis of 2-D discrete-time systems. However, I have the following remarks on the results of this paper.