Several Types Of Stability Problems For Set Differential Systems

Set differential systems as one of the most convenient promotion forms of ordinary differential systems,has important applications in the fields of physics,engineering,control theory,computer and information processing and so on,which makes set control differential systems also attracted high attention.Although there are many results about the existence and stability of solutions for set differential systems.However,the discussion of set control differential systems is mostly about the result of existence.In addition,most of these results are obtained in the case of the classical Hukuhara derivative,whose defect is that the diameter of the obtained solution increasing as time goes.But when considering the second type of Hukuhara derivative,we can obtain the solution of whose diameter decreasing as time goes.Therefore,it is meaningful and worthy to study the set differential systems under the condition of the second type Hukuhara derivative.This paper mainly studies the stability problems of set differential systems with control and the second type Hukuhara derivative by using Lyapunov functions and newly constructed comparison principles.The main context of the paper is composed of four parts.The first two parts discussed the integral 0-stability?the integral 0-stability in terms of two measures the equi-0stability and the 0-practical stability in terms of two measures of set differential systems with control in the case of quasi monotone increasing.And in the last two parts,the second type Hukuhara derivative was introduced to set differential systems,then the equistability of set differential equations with second type Hukuhara derivatives and the practical stability in terms of two measures of fuzzy dynamic equations with second type Hukuhara derivative on Time scales were studied,respectly.