Parametrization of compensators for linear systems with transfer functions of bounded type

A study is made of the feedback stabilization of a plant using a compensator, when the plant and the compensator belong to the class of linear discrete-time systems with matrix-valued transfer functions each entry of which is represented as a quotient of two analytic functions in the Hardy space H_∞. Such transfer functions are called functions of bounded type. A strong notion of right or left coprimeness is provided for the representations of these systems. It is shown that a linear system with a transfer function of bounded type always has a right-coprime representation and a left-coprime representation. Necessary and sufficient conditions are presented for such a plant to be stabilizable by a compensator. It is shown that under the stabilizability condition, it is possible to parameterize the set of all compensators that stabilize the plant