Several Properties of the State of First-order Linear Time-varying Ordinary Differential Systems with Parameters
The article focuses on linear time-varying ordinary differential systems with parameters,investigates the influence of their par-ameter variables on the system state,and explores the properties of the differential system state 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,un-der the condition of non null parameter set,the state set of linear time-varying ordinary differential systems is convex and compact;sec-ondly,in the sense of Hausdorff distance,the state of a time-varying ordinary differential system with parameters is continuous over time.
linear time-varying ordinary differential systemsparametersystem stateconvex tightnesscontinuity
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