广义Lienard方程周期振动同步的判据  

PERIODIC OSCILLATORY SYNCHRONIZATION CRITERIA FOR GENERALIZED LIENARD EQUATION

作　　者：马米花[1] 蔡萍[1] 蔡建平[1] 

机构地区：[1]漳州师范学院数学系,漳州363000

出　　处：《动力学与控制学报》2006年第4期326-331,共6页Journal of Dynamics and Control

基　　金：福建省青年科技人才创新基金项目(2005J054)~~

摘　　要：基于线性时变系统的稳定性理论,李雅普诺夫直接法和Gerschgorin圆盘定理求得判定广义Lienard方程振动系统达到全局同步的几种不同的代数判据.理论上比较这些不同代数判据表明:根据李雅诺夫直接法得到的代数判据优于根据Gerschgorin圆盘定理得到的代数判据,而且通过适当选取李雅普诺夫函数可以得到更优化的代数判据.Rayleigh-Duffing方程作为数值算例进一步验证了理论结果.Algebraic criteria for the periodic oscillatory synchronization of the generalized Lienard systems were derived based respectively on the stability theory of linear time - varied systems, Lyapunov direct method and Gerschgorin disc theorem. It was proven theoretically that the synchronization criteria based on Lyapunov direct method were more flexible than the criteria based on Gerschgorin disc theorem, and the criteria obtained by choosing proper Lyapunov function were more flexible than the criteria based on the stability theory of linear time - varied systems. Rayleigh -Duffing equation as a numerical example verified the theoretical results.

关 键 词：广义LIENARD方程 周期振动同步 代数判据 李雅普诺夫稳定性 

分 类 号：O231[理学—运筹学与控制论]