TY - JOUR
T1 - Global stabilization for systems evolving on manifolds
AU - Malisoff, M.
AU - Krichman, M.
AU - Sontag, E.
N1 - Funding Information:
Acknowledgments. M. Malisoff was supported by Louisiana Board of Re-
Funding Information:
gents Contract LEQSF(2003-06)-RD-A-12 and NSF DMS-0424011. Part of the work of M. Krichman was carried out while this author was a Research Assistant at Rutgers University. Krichman thanks Felipe M. Pait for helpful comments. E. Sontag was supported by NSF Grant CCR-0206789 and NSF DMS-0504557.
PY - 2006/4
Y1 - 2006/4
N2 - We show that any globally asymptotically controllable system on any smooth manifold can be globally stabilized by a state feedback. Since we allow discontinuous feedbacks, we interpret the solutions of our systems in the "sample and hold" sense introduced by Clarke, Ledyaev, Sontag, and Subbotin (CLSS). We generalize their theorem which is the special case of our result for systems on Euclidean space. We apply our result to the input-to-state stabilization of systems on manifolds with respect to actuator errors, under small observation noise.
AB - We show that any globally asymptotically controllable system on any smooth manifold can be globally stabilized by a state feedback. Since we allow discontinuous feedbacks, we interpret the solutions of our systems in the "sample and hold" sense introduced by Clarke, Ledyaev, Sontag, and Subbotin (CLSS). We generalize their theorem which is the special case of our result for systems on Euclidean space. We apply our result to the input-to-state stabilization of systems on manifolds with respect to actuator errors, under small observation noise.
KW - Asymptotic controllability
KW - Control systems on manifolds
KW - Input-to-state stabilization
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U2 - 10.1007/s10450-006-0379-x
DO - 10.1007/s10450-006-0379-x
M3 - Article
AN - SCOPUS:33749389895
VL - 12
SP - 161
EP - 184
JO - Dynamics and Control
JF - Dynamics and Control
SN - 1079-2724
IS - 2
ER -