DUALITIES IN SYSTEMS THEORY –WITH APPLICATION TO DELAY-DIFFERENTIAL SYSTEMS

Two complete and intrinsic definitions of linear systems are existing: (i) in the behavioral approach , a linear system is the kernel B of a matrix-valued operator R in a power of a signal space W; (ii) in the module theoretic setting , a linear system is the cokernel M of R (thus, M is a finitely presented module over a ring of operators). These two formulations have connections and under certain conditions the knowledge of M is equivalent to that of B. The minimal conditions under which such an equivalence exists are investigated in this paper and the case of convolution systems is especially considered.