TY - GEN
T1 - A converse Liapunov theorem for uniformly locally exponentially stable systems admitting Carathéodory solutions
AU - Trumpf, Jochen
AU - Mahony, Robert
PY - 2010
Y1 - 2010
N2 - This paper provides a converse Liapunov theorem for uniformly locally exponentially stable, locally Lipschitz, non-linear, time-varying, possibly non-smooth systems that admit Caratheodory solutions. The main result proves that a critical point of such a system is uniformly locally exponentially stable if and only if the system admits a local (possibly non-smooth, time-varying) Liapunov function.
AB - This paper provides a converse Liapunov theorem for uniformly locally exponentially stable, locally Lipschitz, non-linear, time-varying, possibly non-smooth systems that admit Caratheodory solutions. The main result proves that a critical point of such a system is uniformly locally exponentially stable if and only if the system admits a local (possibly non-smooth, time-varying) Liapunov function.
KW - Caratheodory solution
KW - Converse Liapunov theorem
KW - Uniform local exponential stability
UR - http://www.scopus.com/inward/record.url?scp=80051765816&partnerID=8YFLogxK
U2 - 10.3182/20100901-3-IT-2016.00090
DO - 10.3182/20100901-3-IT-2016.00090
M3 - Conference contribution
SN - 9783902661807
T3 - IFAC Proceedings Volumes (IFAC-PapersOnline)
SP - 1374
EP - 1378
BT - 8th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2010
PB - IFAC Secretariat
ER -