一类非线性组合系统新的稳定性条件  

A New Stability Condition for a Class of Nonlinear Composite Systems

作　　者：刘烨[1] 刘建州[1] 

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105

出　　处：《湖南工业大学学报》2010年第1期50-52,共3页Journal of Hunan University of Technology

基　　金：国家自然科学基金资助项目(10971176)

摘　　要：研究组合大系统存在非线性扰动和不确定性时的稳定性问题。通过对微分方程解的结构研究,应用矩阵相似变换和矩阵指数的特性,将原非线性组合系统的稳定性问题转化为线性系统的稳定性问题。根据线性系统渐近稳定的充分条件,导出了原系统渐近稳定新的判定准则。最后运用数值实例说明了该方法的有效性和可行性。Studies the stability problem of composite systems with nonlinear disturbances and uncertainty. Through the solutions structure of differential equations, matrix similar transformation and matrix exponential properties are applied to translate the stability problem of composite nonlinear systems into that of a linear system. According to linear system sufficient condition for asymptotic stability, deduces a new discriminant criteria for the stability of original systems. Finally, one demonstrative numerical example proves the availability and the effectiveness of the approach.

关 键 词：非线性组合系统 稳定性 微分方程 

分 类 号：O231.2[理学—运筹学与控制论]