A new theorem on higher order derivatives of Lyapunov functions.
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.
Meigoli
Vahid
V
Electrical Engineering Department, Aboureyhan Building, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran. vmeigoly@aut.ac.ir
Nikravesh
Seyyed Kamaleddin Yadavar
SK
D000465:Algorithms; D003198:Computer Simulation; D005246:Feedback; D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted