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

H-Passive Linear Discrete Time Invariant State/Signal Systems

Scheduled for presentation during the Mini-Symposium "Distributed Parameter Systems-I: Operator Theoretic Methods" (MoP06), Monday, July 24, 2006, 16:10−16:35, 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 systems which are passive with respect to a quadratic storage function in the state space, represented by a positive self-adjoint operator H which may be unbounded and have an unbounded inverse. The quadratic supply rate, which describes the energy flow between the system and the surroundings, imposes a Krein space structure on the signal space, but the state space is a Hilbert space. Our main results relate the existence of an operator H > 0 such that the system is H-passive to the existence of a solution of a generalized Kalman-Yakubovich-Popov inequality, and also to the passivity properties of the behavior induced by the system.