基于下确界函数的稳定性定号导函数理论与设计  

THEORY AND DESIGN OF DEFINITE SIGN DERIVATIVE BY LOWER BOUNDARY FUNCTION FOR STABILITY TEST

作　　者：李春文[1] 

机构地区：[1]北京清华大学自动化系

出　　处：《河南科学》1996年第1期1-16,共16页Henan Science

基　　金：国家自然科学基金

摘　　要：通过建立一种基于下确界函数的被称为定号Ｌｉａｐｕｎｏｖ导函数的设计理论与方法，研究了动态系统稳定性的一类新的判定方法。分析了定号导函数的某些性质，与多项式函数的关系，正定性判别，正定性度量，极坐标方法以及υ（ｘ）的正定化算法等基本问题。从而初步形成一个新的、相对系统化的关于稳定性判定的理论框架。In this paper,the theory and design problem of definite-sign derivative function for determining Liapunov stability of dynamical system are studied by lower boundary function. Some existence properties of definite-sign derivative function are discussed. Judge and measurement of positivity, and the method of polynomiarization of multivariable function G(x) or G(θ,r) are derivedin both vertical and polar coordinates. Algorithms of positivarization of derivative function υ(x)are designed. Then a new, primary and relatively systematic theory and design frame of definitesign derivative function is built for dynamical system stability test.

关 键 词：稳定性 定号导函数 下确界函数 动态系统 

分 类 号：O175.13[理学—数学]