Energy-to-peak model reduction for 2-D discrete systems in Fornasini-Marchesini form

In this paper, the problem of constructing a reduced-order model to approximate a Fornasini-Marchesini (FM) second model is considered such that the energy-to-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 parameterization 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 reduced-order models. Finally, an example is employed to demonstrate the effectiveness of the model reduction algorithm.