A new theorem on higher order derivatives of Lyapunov functions
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Published on: August 12, 2013
Vahid Meigoli1, Seyyed Kamaleddin Yadavar Nikravesh
1Electrical Engineering Department, Aboureyhan Building, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran. vmeigoly@aut.ac.ir
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.
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