TY - JOUR
T1 - On the analysis of nonlinear nilpotent switched systems using the Hall-Sussmann system
AU - Margaliot, Michael
PY - 2009/10
Y1 - 2009/10
N2 - We consider an open problem on the stability of nonlinear nilpotent switched systems posed by Daniel Liberzon. Partial solutions to this problem were obtained as corollaries of global nice reachability results for nilpotent control systems. The global structure is crucial in establishing stability. We show that a nice reachability analysis may be reduced to the reachability analysis of a specific canonical system, the nilpotent Hall-Sussmann system. Furthermore, local nice reachability properties for this specific system imply global nice reachability for general nilpotent systems. We derive several new results revealing the elegant Lie-algebraic structure of the nilpotent Hall-Sussmann system.
AB - We consider an open problem on the stability of nonlinear nilpotent switched systems posed by Daniel Liberzon. Partial solutions to this problem were obtained as corollaries of global nice reachability results for nilpotent control systems. The global structure is crucial in establishing stability. We show that a nice reachability analysis may be reduced to the reachability analysis of a specific canonical system, the nilpotent Hall-Sussmann system. Furthermore, local nice reachability properties for this specific system imply global nice reachability for general nilpotent systems. We derive several new results revealing the elegant Lie-algebraic structure of the nilpotent Hall-Sussmann system.
KW - Global asymptotic stability
KW - Lie bracket
KW - Maximum principle
KW - Nilpotent Lie algebra
KW - Nonlinear switched systems
KW - Optimal control
KW - P. Hall basis
KW - Reachability with nice controls
KW - Reachable sets
UR - http://www.scopus.com/inward/record.url?scp=70349470956&partnerID=8YFLogxK
U2 - 10.1016/j.sysconle.2009.07.003
DO - 10.1016/j.sysconle.2009.07.003
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AN - SCOPUS:70349470956
SN - 0167-6911
VL - 58
SP - 766
EP - 772
JO - Systems and Control Letters
JF - Systems and Control Letters
IS - 10-11
ER -