A Distributional-Module Theoretic Representation of Linear Dynamical Continuous-Time Systems

摘要

The document presents a new algebraic representation of linear constant continuous-time dynamical systems without the use of Laplace transform techniques. In particular, new results are given on the realization of multiterminal systems with special emphasis on lumped-distributed systems or networks. The theory begins with a precise definition of linear continuous-time dynamical systems in the input/output behavior of a linear system is defined in terms of a zero state input/output map whose domain and range consist of 'generalized functions' or Schwartz distributions. The fundamental problem of concern here, which is called the problem of realization, is the determination of the internal structure and properties of a linear system given only its zero state input/output map. (Author)