A Stability Criterion for Delay Differential Equations with Impulse Effects
نویسنده
چکیده
In this paper, we prove that if a delay differential equation with impulse effects of the form x (t) = A(t)x(t) + B(t)x(t − τ) , t = θ i , ∆x(θ i) = C i x(θ i) + D i x(θ i−j), i ∈ N, verifies a Perron condition then its trivial solution is uniformly asymptotically stable.
منابع مشابه
Stability of two classes of improved backward Euler methods for stochastic delay differential equations of neutral type
This paper examines stability analysis of two classes of improved backward Euler methods, namely split-step $(theta, lambda)$-backward Euler (SSBE) and semi-implicit $(theta,lambda)$-Euler (SIE) methods, for nonlinear neutral stochastic delay differential equations (NSDDEs). It is proved that the SSBE method with $theta, lambdain(0,1]$ can recover the exponential mean-square stability with some...
متن کاملMathematical Modeling of Cancer Cells and Chemotherapy Protocol Dealing Optimization Using Fuzzy Differential Equations And Lypunov Stability Criterion
Mathematical models can simulate the growth and proliferation of cells in the interaction with healthy cells, the immune system and measure the toxicity of drug and its effects on healthy tissue pay. One of the main goals of modeling the structure and growth of cancer cells is to find a control model suitable for administration among patients. In this study, a new mathematical model is designed...
متن کاملStability analysis of impulsive fuzzy differential equations with finite delayed state
In this paper we introduce some stability criteria for impulsive fuzzy system of differential equations with finite delay in states. Firstly, a new comparison principle for fuzzy differential system compared to crisp ordinary differential equation, based on a notion of upper quasi-monotone nondecreasing, in N dimentional state space is presented. Furthermore, in order to analyze the stability o...
متن کاملStability analysis of nonlinear hybrid delayed systems described by impulsive fuzzy differential equations
In this paper we introduce some stability criteria of nonlinear hybrid systems with time delay described by impulsive hybrid fuzzy system of differential equations. Firstly, a comparison principle for fuzzy differential system based on a notion of upper quasi-monotone nondecreasing is presented. Here, for stability analysis of fuzzy dynamical systems, vector Lyapunov-like functions are defined....
متن کاملOscillation for Nonlinear Hyperbolic Equations with Influence of Impulse and Delay
In this paper, by making use of the calculous technique and some results of the differential inequality, oscillatory properties of the solutions of certain impulsive delay hyperbolic partial differential equations with nonlinear diffusion term are investigated. A new sufficient criterion for oscillations of such equations is obtained.
متن کاملذخیره 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 2007