Abstract
The problem of constructing linear time invariant state space models that are compatible with a given input-output map is examined. The class of models considered includes many systems of an infinite dimensional nature where the control action and sensing are restricted to subsets of the region over which the system is distributed. Concepts of controllability and observability are defined and it is shown how, under certain assumptions, the uncontrollable and unobservable parts of a system may be factored out. The main realization theorem is set in a time domain framework and a detailed analysis of state space isomorphism theory (“uniqueness of realizations”), is presented.
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