Iterative Dual Rational Krylov and Iterative SVD-Dual Rational Krylov Model Reduction for Switched Linear Systems

In this paper, we propose two models reduction algorithms for approximation of large-scale linear switched systems. We present at first the iterative dual rational krylov approach, that construct a union of krylov subspaces. The iterative dual rational Krylov is low in cost, numerical efficient but the stability of reduced system is not always guaranteed. In the second part we present, the iterative SVD-Dual Rational Krylov approach. This method is a combining of two sidedprojections, one side is generated by the dual Rational krylovbased model reduction techniques and the other side is generated by the SVD model reduction techniques, while the SVD-side depends on the observability gramian. This method is numerical efficient, minimize the H∞ Error between the original switched system and reduced one and preserved always the stability of reduced systems. A simulation two examples are considered in order to take a performance study of these proposed approaches.