Generalized gramian framework for model reduction of switched systems

In this paper, a general method for model order reduction of switched linear dynamical systems is presented. The proposed technique is based on the generalized gramian framework for model reduction. It is shown that different classical reduction methods can be developed into generalized gramian framework. Balanced reduction within specified frequency bound is developed within this framework. In order to avoid numerical instability and also to increase the numerical efficiency, generalized gramian based Petrov-Galerkin projection is constructed instead of the similarity transform approach for reduction. The method preserves the stability of the original switched system under arbitrary switching signal and is applicable to both continuous and discrete time systems. The performance of the proposed method is illustrated by numerical examples.