Determination of Morse´s canonical form using the structure algorithm

A computational method for constructing the canonical form of Morse [1] is presented. The canonical form and the underlying structure is important in the solution of singular optimal control and filtering problems. However, Morse´s paper is not complete in the algorithmic sense and that several steps are existence results rather than constructive arguments. In this paper, the input, output, state feedback, output injection and coordinate transformations of the canonical form are found using the left Structure Algorithm [2]. The method reveals the finite and infinite zero structure, determines invertibility and finds weak unobservability and strong reachability subspaces efficiently by exploiting the fine structure of linear multivariable dynamical systems. The numerical aspects of the method are also investigated and a stable algorithm is provided.