Impulsive Stabilization of Functional Differential Equations via Liapunov Functionals

Impulsive stabilization of stochastic functional differential equations

This paper investigates impulsive stabilization of stochastic delay differential equations. Both moment and almost sure exponential stability criteria are established using the Lyapunov–Razumikhinmethod. It is shown that an unstable stochastic delay system can be successfully stabilized by impulses. The results can be easily applied to stochastic systems with arbitrarily large delays. An exampl...

On impulsive fuzzy functional differential equations

In this paper, we prove the existence and uniqueness of solution to the impulsive fuzzy functional differential equations under generalized Hukuhara differentiability via the principle of contraction mappings. Some examples are provided to illustrate the result.

Boundedness of Impulsive Functional Differential Equations via Lyapunov Functional

Differential equations with impulsive effect provide mathematical models for many phenomena and processes in the field of natural sciences and technology. Recently a well developed stability theory of functional differential systems has come into existence [15-21]. Qualitative properties of impulsive differential equations have been intensively researched for years. In [3-11], by using lyapunov...

Impulsive Stabilization of Linear Delay Differential Equations

The paper is concerned with stabilization of a scalar delay differention equation ẋ(t)− m ∑ k=1 Ak(t)x[hk(t)] = 0, t ≥ 0, x(ξ) = φ(ξ), ξ < 0, by introducing impulses in certain moments of time x(τj) = Bjx(τj − 0), j = 1, 2, . . . . Explicit stability results are presented both for the equation with positive coefficients and for the equation with Ak being of arbitrary sign. Supported by Israel M...

Impulsive Functional-differential Equations with Nonlocal Conditions