The state space isomorphism theorem for discrete-time infinite-dimensional systems

Amine N. Chakhchoukh, Mark R. Opmeer

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
155 Downloads (Pure)

Abstract

It is well-known that the state space isomorphism theorem fails in infinite-dimensional Hilbert spaces: there exist minimal discrete-time systems (with Hilbert space state spaces) which have the same impulse response, but which are not isomorphic. We consider discrete-time systems on locally convex topological vector spaces which are Hausdorff and barrelled and show that in this setting the state space isomorphism theorem does hold. In contrast to earlier work on topological vector spaces, we consider a definition of minimality based on dilations and show how this necessitates certain definitions of controllability and observability.
Original languageEnglish
Pages (from-to)105-120
JournalIntegral Equations and Operator Theory
Volume84
Issue number1
Early online date24 Jul 2015
DOIs
Publication statusPublished - Jan 2016

Fingerprint Dive into the research topics of 'The state space isomorphism theorem for discrete-time infinite-dimensional systems'. Together they form a unique fingerprint.

Cite this