TY - GEN

T1 - Passive LTI systems with a time-varying perturbation

AU - Weiss, George

AU - Chen, Jian Hua

N1 - Funding Information:
∗This research was supported by the Israel Science Foundation grant 701/10.

PY - 2012

Y1 - 2012

N2 - We study a time-varying well-posed system resulting from the additive perturbation of the generator of a time-invariant well-posed system. The associated generator family has the form A+G(t), where G(t) is a bounded operator on the state space and G(·) is strongly continuous. We show that the resulting time-varying system (the perturbed system) is well-posed and we investigate its properties. In the particular case when the unperturbed system is scattering passive, we derive an energy balance inequality for the perturbed system. If the operators G(t) are dissipative, then the perturbed system is again scattering passive. We illustrate this theory by using it to formulate the system corresponding to a conductor moving in an electromagnetic field described by Maxwell's equations.

AB - We study a time-varying well-posed system resulting from the additive perturbation of the generator of a time-invariant well-posed system. The associated generator family has the form A+G(t), where G(t) is a bounded operator on the state space and G(·) is strongly continuous. We show that the resulting time-varying system (the perturbed system) is well-posed and we investigate its properties. In the particular case when the unperturbed system is scattering passive, we derive an energy balance inequality for the perturbed system. If the operators G(t) are dissipative, then the perturbed system is again scattering passive. We illustrate this theory by using it to formulate the system corresponding to a conductor moving in an electromagnetic field described by Maxwell's equations.

UR - http://www.scopus.com/inward/record.url?scp=84880967624&partnerID=8YFLogxK

U2 - 10.3182/20120829-3-IT-4022.00020

DO - 10.3182/20120829-3-IT-4022.00020

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AN - SCOPUS:84880967624

SN - 9783902823083

T3 - IFAC Proceedings Volumes (IFAC-PapersOnline)

SP - 126

EP - 131

BT - 4th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, LHMNLC 2012

PB - IFAC Secretariat

T2 - 4th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, LHMNLC 2012

Y2 - 29 August 2012 through 31 August 2012

ER -