TY - GEN
T1 - On three generalizations of contraction
AU - Sontag, Eduardo D.
AU - Margaliot, Michael
AU - Tuller, Tamir
N1 - Publisher Copyright:
© 2014 IEEE.
PY - 2014
Y1 - 2014
N2 - We introduce three forms of generalized contraction (GC). Roughly speaking, these are motivated by allowing contraction to take place after small transients in time and/or amplitude. Indeed, contraction is usually used to prove asymptotic properties, like convergence to an attractor or entrainment to a periodic excitation, and allowing initial transients does not affect this asymptotic behavior. We provide sufficient conditions for GC, and demonstrate their usefulness using examples of systems that are not contractive, with respect to any norm, yet are GC.
AB - We introduce three forms of generalized contraction (GC). Roughly speaking, these are motivated by allowing contraction to take place after small transients in time and/or amplitude. Indeed, contraction is usually used to prove asymptotic properties, like convergence to an attractor or entrainment to a periodic excitation, and allowing initial transients does not affect this asymptotic behavior. We provide sufficient conditions for GC, and demonstrate their usefulness using examples of systems that are not contractive, with respect to any norm, yet are GC.
UR - http://www.scopus.com/inward/record.url?scp=84977892750&partnerID=8YFLogxK
U2 - 10.1109/CDC.2014.7039618
DO - 10.1109/CDC.2014.7039618
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AN - SCOPUS:84977892750
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 1539
EP - 1544
BT - 53rd IEEE Conference on Decision and Control,CDC 2014
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014
Y2 - 15 December 2014 through 17 December 2014
ER -