Iterative Dual Rational Krylov and Iterative SVD-Dual Rational Krylov Model Reduction for Switched Linear Systems - Complex System Modelling and Control Through Intelligent Soft Computations - page 401

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

Kouki Mohamed, Abbes Mehdi and Abdelkader Mami

Abstract Methods reductions of large scale linear time invariant systems are
numerous, include among these which are based on the projection onto the Krylov
subspace (Arnoldi, Lanczos, Arnoldi rational, Lanczos rational, Adaptive rational
Arnoldi, rational Krylov) and methods based on singular values decomposition.
Against, the reduction approaches of large scale switched linear systems are very
limited (LMI, Arnoldi). In this chapter, two model reductions algorithms for
approximation of large-scale linear switched systems are proposed, which are based
on the Krylov subspace on the one hand and on the singular value decomposition
on the other hand. At

first the principle of the Dual rational Krylov based method is
presented, based on this method for presenting at first the iterative dual rational

Krylov approach that constructs a union of Krylov subspaces to generate two
projection matrices. The iterative dual rational Krylov is low in cost, numerically
ef cient but the stability of reduced linear switched system is not always guaran-

teed. In the second part, the iterative SVD-Dual Rational Krylov approach is pre-
sented. This method is a combining of two sided-projections, one side is generated
by the dual Rational Krylov-based 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 numerically ef cient, minimize the H 1

error between the original switched system and reduced one and preserve the
stability of reduced systems. A simulation two examples are considered in order to
take a performance study of these proposed approaches.