A new balanced canonical form for stable multivariable systems

Abstract

A new balanced canonical form is presented for stable multivariable linear systems. Overlapping continuous block-balanced canonical forms were introduced by Hanson-Ober for the stable single-input/single-output (SISO) case as a generalisation of the balanced canonical form introduced by Ober (1987) for the SISO case. In the search for a generalization of these results to the multivariable case a new multivariable balanced canonical form was discovered, which is of interest in its own right and is presented in this paper. The new canonical form has a number of nice properties. The integer invariants that appear in the canonical form are the multiplicities of the Hankel singular values and a number of new invariants, which are in one-to-one objective correspondence with the Kronecker indexes of subsystems. Truncation of the state vector leads to stable minimal models in canonical form. In the SISO case the canonical form coincides with Ober's balanced canonical form. The reachability matrix of a system in canonical form with identical singular values is positive upper triangular. >