Several Properties for the Statements of First-order Linear Time-varying Ordinary Differential System with a Algorithm of Parameter Set

In this paper, to the first-order linear time-varying ordinary differential systems, the properties of the statements are explored with a parameter algorithm, in which the effect of parameter set on the statements of systems are studied by convex combination of the parameters in parameter set according to the formula for the solution of systems for Caratheodory lemma and Filippov lemma. With the algorithm, two main results are obtained basing on the properties of the parameter sets and Hausdorff metric of points set, one is the statement sets of the system are compact and convex if the parameter sets are compact and not null; the other is statements of the first-ordered linear time-vary ordinary differential systems with parameters are continuous according to the time t in the sense of Hausdorff metric.