Lyapunov-razumikhin Method for Differential Equations with Piecewise Constant Argument

نویسندگان

  • Marat Akhmet
  • Duygu Aruğaslan
  • Hans-Otto Walther
  • DUYGU ARUĞASLAN
چکیده

At the first time, Razumikhin technique is applied for differential equations with piecewise constant argument of generalized type [1, 2]. Sufficient conditions are established for stability, uniform stability and uniform asymptotic stability of the trivial solution of such equations. We also provide appropriate examples to illustrate our results.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Lyapunov-razumikhin Method for Asymptotic Stability of Sets for Impulsive Functional Differential Equations

In the present paper, we study the global stability of sets of sufficiently general type with respect to impulsive functional differential equations with variable impulsive perturbations. The main results are obtained by means of piecewise continuous Lyapunov functions and the use of the Razumikhin technique.

متن کامل

Impulsive Stabilization of certain Delay Differential Equations with Piecewise Constant Argument

In this paper, we investigate the impulsive stabilization of certain delay differential equations with piecewise constant argument by using Lyapunov function and analysis methods. Some nonimpulsive systems can be stabilized by imposition of impulsive controls. We also give an example to demonstrate the effectiveness of the proposed control and stabilization methods. AMS Subject Classifications:...

متن کامل

Impulsive Stabilization of a Class of Stochastic Functional Differential Equations with Time Delays

This paper investigates the pth moment globally uniformly exponential stability of a class of impulsive stabilization of stochastic delay differential equations,and the pth moment exponential stability criteria is established by using theLyapunov–Razumikhin method. Keywords—Stochastic delay differential equations; Exponential stability ; Lyapunov-Razumikhin method ; Impulsive control

متن کامل

Asymptotic equivalence of differential equations with piecewise constant argument

By using the method of investigation of differential equations with piecewise constant argument and some integral inequalities of Gronwall type we obtain some results of asymptotic equivalence of the stable solutions of some differential equations with piecewise constant argument. Our results generalize and improve some recent results. AMS subject classifications: 34K25, 34K34

متن کامل

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...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009