Stability Of Impulsive Differential Equations Research Articles

Variation of parameters and initial time difference Lipschitz stability of impulsive differential equations

In this paper, we investigate the Lipschitz stability of a perturbed impulsive differential system concerning the unperturbed system. We employ the variation of parameters or the constant of variation for impulsive differential systems with an initial time difference.

Uniqueness of solutions and linearized stability for impulsive differential equations with state-dependent delay

We prove that under fairly natural conditions on the state space and nonlinearities, it is typical for an impulsive differential equation with state-dependent delay to exhibit non-uniqueness of solutions. On a constructive note, we show that uniqueness of solutions can be recovered using a Winston-type condition on the state-dependent delay. Irrespective of uniqueness of solutions, we prove a result on linearized stability. As a specific application, we consider a scalar equation on the positive half-line with continuous-time negative feedback, non-negative state-dependent delayed nonlinearity and impulse effect functional satisfying affine bounds.

Chaotic Synchronization in Models of Impulsive Power Systems with Delay

Global complete chaos synchronization in impulsive power systems with delay is studied. The sufficient conditions of exponential synchronization are established based on the theory of stability of impulsive differential equations with delay. Illustrative examples that demonstrate the applicability and effectiveness of the obtained results are given.

Mittag-Leffler stability of impulsive differential equations of fractional order

Mittag-Leffler stability of impulsive differential equations of fractional order

Oscillation and stability of first-order delay differential equations with retarded impulses

In this paper, we study both the oscillation and the stability of impulsive differential equations when not only the continuous argument but also the impulse condition involves delay. The results obtained in the present paper improve and generalize the main results of the key references in this subject. An illustrative example is also provided.

A note on stability of impulsive differential equations

In this note, we study a new class of ordinary differential equations with non-instantaneous impulses. Both existence and generalized Ulam-Hyers-Rassias stability results are established. Finally, an example is given to illustrate our theoretical results.

On the Practical Stability of Impulsive Differential Equations with Infinite Delay in Terms of Two Measures

We consider the practical stability of impulsive differential equations with infinite delay in terms of two measures. New stability criteria are established by employing Lyapunov functions and Razumikhin technique. Moreover, an example is given to illustrate the advantage of the obtained result.

Global exponential stability of impulsive differential equations with any time delays

The main objective of this letter is to further investigate the global exponential stability of a class of general impulsive retarded functional differential equations. Several new criteria on global exponential stability are analytically established based on Lyapunov function methods combined with Razumikhin techniques. The obtained results extend and generalize some results existing in the literature. An example, along with computer simulations, is included to illustrate the results.

P-moment stability of stochastic impulsive differential equations and impulsive synchronization of Lorenz system excited by parameter white-noise

In this paper, the p-moment stability of impulsive differential equations is considered. A theory about this problem under a weak condition and an assumption which is more familiar in impulsive system is proved. As an application, the impulsive synchronization of Lorenz system excited by white-noise is considered, the p-moment stability of error system is proved, so the synchronization can be realized using impulsive method under p-moment stability. Numerical simulation verify the feasibility of this synchronization method.

Strict Stability of Impulsive Differential Equations

In this paper, we will extend the strict stability to impulsive differential equations. By using Lyapunov functions, we will get some criteria for the strict stability of impulsive differential equations, and we can see that impulses do contribute to the system's strict stability behavior. An example is also given in this paper to illustrate the efficiency of the obtained results.

Eventual practical stability of impulsive differential equations with time delay in terms of two measurements

In this paper we introduce a new stability—eventual practical stability for impulsive differential equations with time delay. By using Lyapunov functions and comparison principle, we will get some criteria of eventual practical stability, eventual practical quasistability and strong eventual practical stability for impulsive differential equations with time delay in terms of two measurements.

On the general problem of stability for impulsive differential equations

Criteria for stability, asymptotical stability and instability of the nontrivial solutions of the impulsive system dx dt =f(t,x), t≠θ i(x),Δx| t=θ i(x) =I i(x), i∈ N={1,2,…}, where Δx| t= θ := x( θ+)− x( θ), x( θ+)=lim t→ θ + x( t) are obtained by Lyapunov's second method. The construction of a reduced system in the neighbourhood of a nontrivial solution is a central auxiliary result of the paper.