含参量一阶线性时变常微分系统状态的几个性质

Several Properties of the State of First-order Linear Timevarying Ordinary Differential Systems with Parameters

文章针对含参量线性时变常微分系统,研究其参变量对系统状态的影响,并探求含参变量的微分系统状态的性质。基于参变量集合的特点和点集Hausdorff距离,主要得到以下两方面的结果:其一,在参变量集非空条件下,线性时变常微分系统状态集是凸紧的;其二,在Hausdorff距离意义下,含参量时变常微分系统的状态依时间是连续的。

The article focuses on linear time-varying ordinary differential systems with parameters,investigates the influence of their parameter variables on the systemstate,and explores the properties of the differential systemstate with parameter variables.Based on the characteristics of the parameter set and the Hausdorff distance of the point set,the following two results are mainly obtained:firstly,under the condition of non null parameter set,the state set of linear time-varying ordinary differential systems is convex and compact;secondly,in the sense of Hausdorff distance,the state of a time-varying ordinary differential systemwith parameters is continuous over time.