Stability Analysis For Some Kinds Of Set Differential Equations

This paper mainly discusses the stability of several kinds of set differential equations.As the development of the theory of set differential equations,many scholars have studied the theory of set differential equations in depth.In the study of set differential equations,when the set is a single valued mapping,the Hukuhara derivative and integral in set differential equations are simplified to ordinary vector derivative and the integral.Therefore,ordinary differential equations are special cases of set differential equations.On the other hand,when the multivalued differential inclusion does not have convexity,the multivalued differential inclusion can be converted into set differential equations to be considered.Therefore,set differential equations can be used as a tool to study the multivalued differential inclusion.With the in-depth study of the stability of differential equations,many new concepts of stability have appeared.For example,practical stability,strict practical stability,stability in terms of two measures and so on.The main contents are as follows:Firstly,the practical stability of the impulsive set differential equations with the Causal operator is studied,the heterogeneous matrix-value Lyapunov function is defined,and the practical stability of the initial value problem of the equations is studied by using the heterogeneous matrix-value Lyapunov method and the comparison principle.Secondly,the definition of the sheaf solution of impulsive set differential equations is given.Then the strict practical stability in terms of two measures and strict practical stability of the solution and sheaf solution of the initial value problem of impulsive set differential equations are studied by the Lyapunov method and the comparison principle.Finally,the practical stability in terms of two measures of set differential equations involving memoried Causal operators with second type Hukuhara derivative is studied.By introducing the notion of upper quasi-monotone nondecreasing,the practical stability in terms of two measures of the initial value problem of the equations is studied by using the vector Lyapunov method and the comparison principle.