The Lanczos-Arnoldi algorithm and controllability (Q799621)

The controllable subspace of linear systems described by the mathematical model \(\dot x=Ax+Bu\) is usually determined by the so-called staircase algorithm. In order to apply this method, it is necessary to store the matrix A as a full matrix, even if it is large and sparse. With the algorithms described in the paper equivalent results are obtained with reduced storage requirements. The methods are based on orthogonalizing the Krylov-sequences. The main difference to the staircase method consists in the proposed orthogonalization procedure. Results from numerical experiments are presented.