Linear Delay-Differential Systems with Commensurate Delays: An Algebraic Approach

Introduction.- The Algebraic Framework.- The Algebraic Structure of H_0. Divisibility Properties. Matrices over H_0. Systems over Rings: A Brief Survery. The Nonfinitely Generated Ideals of H_0. The Ring H as a Convolution Algebra. Computing the Bezout Identity.- Behaviors of Delay-Differential Systems. The Lattice of Behaviors. Input/Output Systems. Transfer Classes and Controllable Systems. Subbehaviors and Interconnections. Assigning the Characteristic Function. Biduals of Nonfinitely Generated Ideals.- First-Order Representations. Multi-Operator Systems. The Realization Procedure of Fuhrmann. First-Order Realizations. Some Minimality Issues.