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A new definition of the $\mathcal{H}_2$ norm for linear switched systems isintroduced. It is based on appropriately defined time-domain kernels, orequivalently, on infinite controllability and observability Gramian matrices.Furthermore, an extension of the iterative rational Krylov algorithm to theclass of linear switched systems is proposed.

On the $\mathcal{H}_2$ norm and iterative model order reduction of linear switched systems