Kalman decomposition of linear fractional transformation representations and minimality

A method of decomposing systems captured as linear fractional transformations on noncommuting operators into a Kalman type of decomposition is presented. By considering the operators as acting on vector valued discrete time signals, we generalize the standard notions of controllability and observability to the uncertain case. These notions can then be used to establish the minimality of a given representation, and form the basis for tractable algorithms which can be used to construct minimal representations