TY - JOUR

T1 - The state space isomorphism theorem for discrete-time infinite-dimensional systems

AU - Chakhchoukh, Amine N.

AU - Opmeer, Mark R.

PY - 2016/1

Y1 - 2016/1

N2 - 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.

AB - 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.

UR - http://dx.doi.org/10.1007/s00020-015-2251-4

U2 - 10.1007/s00020-015-2251-4

DO - 10.1007/s00020-015-2251-4

M3 - Article

VL - 84

SP - 105

EP - 120

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 1

ER -