TY - GEN
T1 - An internal model principle for observers
AU - Trumpf, Jochen
AU - Trentelman, Harry L.
AU - Willems, Jan C.
PY - 2011
Y1 - 2011
N2 - This paper deals with the observer problem for dynamical systems in a behavioral context. We are given a dynamical system together with a partition of the system variables into a set of known or measured variables and a set of unknown, to be estimated variables. The observer problem is to find a system that produces an estimate of the unknown variables on the basis of the known or measured variables. For a given plant and partition, we establish a characterization of all error behaviors that can be achieved by interconnecting the plant with some observer. The main result of this paper is a very general, behavioral formulation of an internal model principle for observers. We will show that a nonintrusive observer achieves a stable error behavior if and only if, in addition to a detectability condition on the observer, the observer behavior contains the controllable part and the antistable part of some autonomous part of the plant behavior.
AB - This paper deals with the observer problem for dynamical systems in a behavioral context. We are given a dynamical system together with a partition of the system variables into a set of known or measured variables and a set of unknown, to be estimated variables. The observer problem is to find a system that produces an estimate of the unknown variables on the basis of the known or measured variables. For a given plant and partition, we establish a characterization of all error behaviors that can be achieved by interconnecting the plant with some observer. The main result of this paper is a very general, behavioral formulation of an internal model principle for observers. We will show that a nonintrusive observer achieves a stable error behavior if and only if, in addition to a detectability condition on the observer, the observer behavior contains the controllable part and the antistable part of some autonomous part of the plant behavior.
UR - http://www.scopus.com/inward/record.url?scp=84860672334&partnerID=8YFLogxK
U2 - 10.1109/CDC.2011.6160666
DO - 10.1109/CDC.2011.6160666
M3 - Conference contribution
SN - 9781612848006
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 3992
EP - 3999
BT - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Y2 - 12 December 2011 through 15 December 2011
ER -