Module Structure of Infinite-Dimensional Systems with Applications to Controllability

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Abstract
A theory of infinite-dimensional time-invariant continuous-time systems is developed in terms of modules defined over a convolution ring of generalized functions. In particular, input/output operators are formulated as module homomorphisms between free modules over the convolution ring, and systems are defined in terms of a state module. Results are presented on causality and the problem of realization. The module framework is then utilized to study the reachability and controllability of states and outputs: New results are obtained on the smoothness of controls, bounded-time controls, and minimal-time controls.