Energy-to-Peak Model Reduction for 2-D Discrete Systems in Fornasini-Marchesini Form *

In this paper, the problem of constructing a reducedorder model to approximate a Fornasini-Marchesini (FM) second model is considered such that the energyto- peak gain of the error model between the original FM second model and reduced-order one is less than a prescribed scalar. First, a sufficient condition to characterize the bound of the energy-to-peak gain of FM second models is presented in terms of linear matrix inequalities (LMIs). Then, a parametrization of reduced-order models that solve the energy-to-peak model reduction problem is given. Such a problem is formulated in the form of LMIs with inverse constraint. An efficient algorithm is derived to obtain the reducedorder models. Finally, an example is employed to demonstrate the effectiveness of the model reduction algorithm.