Perturbation analysis of system hessenberg and hessenberg-triangular forms Original Research Article

Laub and Linnemann have shown by numerous examples that the system Hessenberg form of a single-input controllable system can be extremely sensitive to perturbations. However, the question as to which quantities can be used to assess the condition of the system Hessenberg form remains unanswered. This paper gives an answer to this question. Perturbation bounds and condition numbers for the system Hessenberg form of a single-input controllable system are derived in various ways. Moreover, this paper also derives perturbation bounds and condition numbers for the Hessenberg-triangular form of a more general single-input controllable system.