Uniform Strict Practical Stability Criteria for Impulsive Functional Differential Equations

Abstract

Strict stability is the kind of stability that can give us some information about the rate of decay of the solution. There are some results about strict stability of functional differential equations. On other hand, in the study of stability, an interesting set of problems deal with bringing sets close to a certain state, rather than the equilibrium state. The desired state of a system may be mathematically unstable and yet the system may oscillate sufficiently near this state that its performance is acceptable. Many problems fall into this category. Such considerations led to the notion of practical stability which is neither weaker nor stronger than stability. In this paper, strict practical stability of Impulsive functional differential equations in which the state variables on the impulses are related to time delay is considered. By using Lyapunov functions and Razumikhin technique, some criteria for strict practical stability for functional differential equations, in which the state variables on the impulses are related to the time delay, are provided.