Generalized Gramian Framework for Model/Controller Order Reduction of Switched Systems

In this article, a general method for model/controller order reduction of switched linear dynamical systems
is presented. The proposed technique is based on the generalised gramian framework for model reduction. It is
shown that different classical reduction methods can be developed into a generalised gramian framework.
Balanced reduction within a specified frequency bound is developed within this framework. In order to avoid
numerical instability and also to increase the numerical efficiency, generalised gramian-based Petrov–Galerkin
projection is constructed instead of the similarity transform approach for reduction. The framework is developed
for switched controller reduction. To the best of our knowledge, there is no other reported result on switched
controller reduction in the literature. The method preserves the stability under an arbitrary switching signal for
both model and controller reduction. Furthermore, it is applicable to both continuous and discrete time systems
for different classical gramian-based reduction methods. The performance of the proposed method is illustrated
by numerical examples.