Meigoli Vahid, Nikravesh Seyyed Kamaleddin Yadavar
Electrical Engineering Department, Aboureyhan Building, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran.
ISA Trans. 2009 Apr;48(2):173-9. doi: 10.1016/j.isatra.2009.01.001. Epub 2009 Feb 3.
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.
非线性动态系统的李雅普诺夫稳定性分析方法要求李雅普诺夫函数沿系统轨迹的一阶导数非正。本文提出了一种新方法来放宽这一要求。针对非线性系统的稳定性分析，提出了一个新的充分条件，引入了一些关于李雅普诺夫函数高阶导数的不等式。这些微分不等式可被视为一个具有负输入的新型可控标准型线性时不变系统。然后，将给定非线性系统的稳定性分析简化为检查新线性时不变系统的特征方程是否为赫尔维茨方程。通过一些例子来阐述该方法。
