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
SN - 0378-620X
VL - 84
SP - 105
EP - 120
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
IS - 1
ER -