Module Structure of Infinite-Dimensional Systems with Applications to Controllability.

摘要

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. (Author)