Nearly minimal reduced order systems

Given a MIMO system we seek a full or partial realization of it that is in convenient form. One important application is to obtain a frequency response plot. Here we describe stable methods to produce a fishbone matrix which provides most of the benefits of a tridiagonal system matrix. A fishbone matrix is tridiagonal except for some extra rows or columns which form the bones of the fish. The idea behind the method is to change the two-sided Lanczos process when an instability is encountered, but to make the modifications as mild as possible. The two-sided Lanczos algorithm attempts to reduce A to tridiagonal form J.