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Stability analysis of generalized impulsive functional differential equations. (English) Zbl 1255.34077
Summary: The stability problem for a class of generalized impulsive functional differential equations in which the state variables on the impulses are related to the time delay is studied. By using Lyapunov functions and Razumikhin techniques, several global exponential stability and uniform stability criteria are derived, which can be applied to impulsive functional differential equations with any time delays. The results obtained improve and extend those in earlier publications. Moreover, our results show that delay differential equations can be exponentially stabilized by impulses in which the state variables are related to the time delay. Finally, two examples are given to illustrate the effectiveness and advantages of the results obtained.
34K20Stability theory of functional-differential equations
34K45Functional-differential equations with impulses
93D05Lyapunov and other classical stabilities of control systems