TY - JOUR
T1 - Stabilization of the inverted pendulum via a constructive lyapunov function
AU - Aguilar-Ibáñez, Carlos
AU - Suarez-Castanon, Miguel S.
N1 - Funding Information:
This research was supported by the Centro de Investigación en Computación of the Instituto Politecnico Nacional (CIC-IPN), and by the Secretaría de Investigación y Posgrado of the Instituto Politecnico Nacional (SIP-IPN), under Research Grants 20091430 and 20091696.
PY - 2010/7
Y1 - 2010/7
N2 - A constructive control strategy for the stabilization of the inverted pendulum system is presented, under the assumption that the pendulum is initialized above the upper half plane. To do so, a suitable procedure to find a candidate Lyapunov function for the whole system is developed. Then, the control is proposed directly from the Lyapunov function, in such a way that its time derivative is semi-definite negative with respect to a convenient manifold. Finally, the asymptotically stability of the closed-loop system is concluded by LaSalle theorem.
AB - A constructive control strategy for the stabilization of the inverted pendulum system is presented, under the assumption that the pendulum is initialized above the upper half plane. To do so, a suitable procedure to find a candidate Lyapunov function for the whole system is developed. Then, the control is proposed directly from the Lyapunov function, in such a way that its time derivative is semi-definite negative with respect to a convenient manifold. Finally, the asymptotically stability of the closed-loop system is concluded by LaSalle theorem.
KW - Inverted pendulum
KW - Lyapunov method
KW - Nonlinear dynamics
UR - http://www.scopus.com/inward/record.url?scp=77953568659&partnerID=8YFLogxK
U2 - 10.1007/s10440-009-9527-0
DO - 10.1007/s10440-009-9527-0
M3 - Artículo
SN - 0167-8019
VL - 111
SP - 15
EP - 26
JO - Acta Applicandae Mathematicae
JF - Acta Applicandae Mathematicae
IS - 1
ER -