A Lyapunov function proof of Poincare's theorem
Tóm tắt
One of the most fundamental results in analyzing the stability properties of periodic orbits and limit cycles of dynamical systems is Poincare's theorem. The proof of this result involves system analytic arguments along with the Hartman-Grobman theorem. In this paper, using the notions of stability of sets, we construct lower semicontinuous Lyapunov functions to provide a Lyapunov function proof of Poincare's theorem.
Từ khóa
#Orbits #Trajectory #Aerospace engineering #Stability analysis #Limit-cycles #Lyapunov method #Sufficient conditions #Mechanical factorsTài liệu tham khảo
leonessa, 2000, Hierarchical Nonlinear Switching Control Design with Applications to Propulsion Systems
10.1007/978-3-642-62006-5
filippov, 1988, Differential Equations With Discontinuous Right-Hand Side Mathematics and its Applications (Soviet Series), 10.1007/978-94-015-7793-9
coddington, 1955, Theory of Ordinary Differential Equations
10.1109/9.898692
10.1109/9.898695
hartman, 1973, Ordinary Differential Equations
khalil, 1996, Nonlinear Systems