title: A new theorem on higher order derivatives of Lyapunov functions.
abstract: The Lyapunov stability analysis method for nonlinear dynamic systems requires a non positive first derivative of the Lyapunov functions along the system's trajectories. In this paper, a new method is developed to relax this requirement. A new sufficient condition is developed for the stability analysis of nonlinear systems, introducing some inequalities for higher order derivatives of the Lyapunov function. The differential inequalities can be considered as a new controllable canonical form linear time invariant system with negative inputs. The stability analysis of a given nonlinear system is then reduced to check if the characteristic equation for the new linear time invariant system is Hurwitz. Some examples are presented to establish the approach.
authors.affiliation: Electrical Engineering Department, Aboureyhan Building, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran. vmeigoly@aut.ac.ir
authors.forename: Vahid
authors.initials: V
authors.lastname: Meigoli
authors.forename: Seyyed Kamaleddin Yadavar
authors.initials: SK
authors.lastname: Nikravesh
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D005246:Feedback; D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted