Title :
A generalization of Poincare´s theorem to hybrid and impulsive dynamical systems
Author :
Nersesov, Sergey G. ; Chellaboina, VijaySekhar ; Haddad, Wassim M.
Author_Institution :
Sch. of Aerosp. Eng., Georgia Inst. of Technol., Atlanta, GA, USA
Abstract :
Poincare´s method is well known for analyzing the stability of continuous-time dynamical systems with periodic solutions by studying the stability properties of a fixed point as an equilibrium point of a discrete-time system. In this paper we generalize Poincare´s method to dynamical systems possessing left-continuous flows to address the stability of limit cycles and periodic orbits of left-continuous, hybrid, and impulsive dynamical systems.
Keywords :
discrete time systems; limit cycles; periodic control; stability; time-varying systems; Poincare theorem; continuous-time dynamical systems; discrete-time system; hybrid impulsive dynamical systems; left-continuous dynamical systems; left-continuous flows; limit cycles; periodic orbits; periodic solutions; stability analysis; Aerospace engineering; Limit-cycles; Mechanical factors; Nonlinear systems; Orbits; Stability analysis; State-space methods; Sufficient conditions; Trajectory;
Conference_Titel :
American Control Conference, 2002. Proceedings of the 2002
Print_ISBN :
0-7803-7298-0
DOI :
10.1109/ACC.2002.1023189
