Arov, Damir Z (South-Ukrainian Pedagogical Univ.), Staffans, Olof (Åbo Akademi)

Affine Input/State/Output Representations of State/Signal Systems

Scheduled for presentation during the Mini-Symposium "Distributed Parameter Systems-I: Operator Theoretic Methods" (MoP06), Monday, July 24, 2006, 15:45−16:10, Room G

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 25, 2024

Abstract

A linear state/signal system in discrete time has a state space X and a signal space W, where the state space is used to represent internal properties of the system, and the signal space describes interactions with the surrounding world. It resembles an input/state/output system apart from the fact that inputs and outputs are not separated from each other. By decomposing the signal space W into a direct sum of an input space U and an output space Y one gets a standard input/state/output system, provided the decomposition is admissible. Here we discuss the nonadmissible case. Instead of ordinary input/state/output representations of the system we then get right and left affine representations, both of the system itself, and of the corresponding transfer function. In particular, in the case of a passive system we get right and left coprime representations of the generalized transfer functions corresponding to nonadmissible decompositions of the signal space, and we end up with transfer functions which are, e.g., generalized Potapov or Nevanlinna class functions.