TY - GEN
T1 - Nonlinear perturbation of a class of conservative linear system
AU - Singh, Shantanu
AU - Weiss, George
N1 - Publisher Copyright:
© 2022 IEEE.
PY - 2022
Y1 - 2022
N2 - In this article we show the existence and uniqueness of classical and generalized solutions of a class of nonlinear infinite dimensional systems. Such systems are obtained by modifying the second order differential equation that is part of the description of conservative linear systems "out of thin air"introduced by M. Tucsnak and G. Weiss in 2003. The modified system contains a new nonlinear damping term, that is maximal monotone and possibly set-valued and hence state trajectories obey a differential inclusion. We show that this new class of nonlinear infinite dimensional systems is incrementally scattering passive (hence well-posed). The proof is based on the Crandall-Pazy theorem which shows that the Lax-Phillips type nonlinear semigroup (that represents the entire system) is a contraction.
AB - In this article we show the existence and uniqueness of classical and generalized solutions of a class of nonlinear infinite dimensional systems. Such systems are obtained by modifying the second order differential equation that is part of the description of conservative linear systems "out of thin air"introduced by M. Tucsnak and G. Weiss in 2003. The modified system contains a new nonlinear damping term, that is maximal monotone and possibly set-valued and hence state trajectories obey a differential inclusion. We show that this new class of nonlinear infinite dimensional systems is incrementally scattering passive (hence well-posed). The proof is based on the Crandall-Pazy theorem which shows that the Lax-Phillips type nonlinear semigroup (that represents the entire system) is a contraction.
UR - http://www.scopus.com/inward/record.url?scp=85147018864&partnerID=8YFLogxK
U2 - 10.1109/CDC51059.2022.9992485
DO - 10.1109/CDC51059.2022.9992485
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AN - SCOPUS:85147018864
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 396
EP - 402
BT - 2022 IEEE 61st Conference on Decision and Control, CDC 2022
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 61st IEEE Conference on Decision and Control, CDC 2022
Y2 - 6 December 2022 through 9 December 2022
ER -