An Approach for Stability-Preserving Model Order Reduction for Switched Linear Systems Based on Individual Subspaces

We present an approach for the stability-preserving model order reduction of switched linear systems with individual subspaces for arbitrary switching signals. First the high-order subsystems of the switched system are reduced by any reduction method and stabilized if necessary. Then the reduced subsystems are made contractive by solving low-dimensional Lyapunov equations. During time simulation the reduced state vector of the active subsystem has to be initialized by the last state vector of the previously active subsystem at the switching points so that the Lyapunov function of the reduced switched system does not grow. This method has no constraints for the structure of the high-order switched systems. The performance of the proposed approach is demonstrated on the basis of a numerical example.