PARAMETRIZATION OF MULTIVARIABLE SYSTEMS USING OUTPUT INJECTIONS - ALPHA-CANONICAL FORMS

In this paper the parametrization of multi-output systems is considered. The method developed is based on the notion of output injections. A similar method has also been used in connection with the identification of a special class of systems. There, the resulting canonical form is called the alpha-canonical form. Here, using the same terminology, we address the following issues on the alpha-canonical form. First, we show that the alpha-canonical forms can be used to parametrize a more general class of systems, namely all minimal (reachable and observable) systems. This is achieved by the use of isomorphisms of the output space. Then, it is proven that the output injections used in constructing the alpha-canonical forms need to have a special structure in order to guarantee the uniqueness of the parametrization. This result also reveals the key role played by dead-beat observers in constructing the alpha-canonical forms. Finally, the connections between the alpha-canonical forms and input-output relations are investigated.