On Stability Problems Of Perturbed Differential Equations

This thesis is devoted to the study of stability problems of perturbed differential equations. The research work focuses mainly on five parts.In Chapter 1, the history of the study and some present work on stability problems of perturbed differential equations are summarized, and the main work of this paper is introduced.In Chapter 2, h-stability for linear matrix differential systems is discussed by cm-ploying the Kronecker product of matrices. and some sufficient conditions are gained.In Chapter 3,h-stability of nonlinear matrix differential systems is investigated by using Lyapunov function and Kronecker product of matrices. Some criteria are obtained, and at the same time, an example is given to illustrate the result.In Chapter 4, we extend the notion of h-stability to differential systems with initial time difference, namely initial time difference h-stability (ITDhS) and then establish several stability criteria of such differential systems by using the method of variation of parameters. At the same time, an example is given.In Chapter 5, we develop variation of parameters formula for impulsive differential equations with initial time changed and use one of the results to study Lipschitz stability.