On the $\mathcal{H}_2$ norm and iterative model order reduction of linear switched systems
This work provides a theoretical foundation and practical algorithm for model order reduction of linear switched systems, addressing a gap in control theory for hybrid dynamical systems.
The paper introduces a new definition of the H2 norm for linear switched systems using time-domain kernels and Gramian matrices, and extends the iterative rational Krylov algorithm for model order reduction to this class. The proposed method achieves efficient reduction while preserving system properties.
A new definition of the $\mathcal{H}_2$ norm for linear switched systems is introduced. It is based on appropriately defined time-domain kernels, or equivalently, on infinite controllability and observability Gramian matrices. Furthermore, an extension of the iterative rational Krylov algorithm to the class of linear switched systems is proposed.