A Note on Shifted Hessenberg Systems and Frequency Response Computation
In this article, we propose a numerical algorithm for efficient and robust solution of a sequence of shifted Hessenberg linear systems. In particular, we show how the frequency response G(sigma) = d - C(A - sigma I)(-1)b in the single input case can be computed more efficiently than with other state-of-the-art methods. We also provide a backward stability analysis of the proposed algorithm.
frequency response algorithms reliability theory computer-aided control system design control theory controller hessenberg form shifted linear systems