非线性广义系统稳定性的数值分析  

Numerical Analysis of Stability of Nonlinear Generalized System

作　　者：徐厚生[1] 张庆灵[2] 

机构地区：[1]沈阳建筑大学理学院,辽宁沈阳110168 [2]东北大学理学院,辽宁沈阳110004

出　　处：《沈阳建筑大学学报（自然科学版）》2008年第1期173-176,共4页Journal of Shenyang Jianzhu University：Natural Science

基　　金：国家自然科学基金项目(60574011)

摘　　要：目的提出一种采用数值分析的方法解决非线性广义系统的稳定性问题.方法从初始条件出发,在一定时间长度上,采用微分方程数值积分法、代数迭代和优化方法来求解系统响应,获得非线性广义系统稳定性的数值分析方法.结果通过数值分析方法对非线性广义系统状态量求解,由终止时刻的状态量可判定系统是否稳定,建立判断性规则.结论以直接数值计算方式探讨广义非线性系统问题求解和稳定性分析判定,为简化稳定性问题分析提供新方法.Numerical analysis method of stability of nonlinear generalized system is studied. Based on initial condition, during certain time span, numerical analysis method of differential equation, algebra iteration and optimization method are used to solve response of generalized system and to analyze stability of generalized system. Through numerical computation, state variable of nonlinear generalized system is analyzed and the model of state variable in ending time is decided and the rule of stability about the system is completed. The conclusion shows that numerical method offers a new manner to simplify the stability of the system.

关 键 词：广义非线性系统 响应 系统稳定性 优化算法 

分 类 号：O175.8[理学—数学]