Model Reduction of Switched Systems Based on Switching Generalized Gramians

In this paper, a general method for model order reduction of discrete-time switched linear systems is presented. The proposed technique uses switching generalized gramians. It is shown that several classical reduction methods can be developed into the generalized gramian framework for the model reduction of linear systems and for the reduction of switched systems. Discrete-time balanced reduction within a specified frequency interval is taken as an example within this framework. To avoid numerical instability and to increase the numerical efficiency, a generalized gramian-based Petrov-Galerkin projection is constructed instead of the similarity transform approach for reduction. It is proven that the proposed reduction framework preserves the stability of the original switched system. The performance of the method is illustrated by numerical examples.