Abstract
Lyapunov functions are a mathematical generalization of the dissipative energy concept of physics. Lyapunov functions are the centerpiece of the Lyapunov-stability theory for dynamical systems in general. Here we present a simple method for checking the validity of a quadratic Lyapunov function, which is constructed for the linearization of a nonlinear system and does not in general satisfy the condition of having a negative orbital derivative on the origins basin of attraction. The current work also extends previous work done on continuous and piecewise afine (CPA) Lyapunov functions by permitting more general triangulations than have been used in that context, namely Delaunay triangulations. Delaunay triangulations have been studied intensively in the literature and allow local refinements of the triangulation. The third contribution of this paper is a freely available MATLAB implementation of the methods proposed.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
