[PDF] Top 20 Strict Stability Criteria for Impulsive Functional Differential Systems

... time-delay systems are frequently encountered in engineering, biology, economy, and other disciplines, it is significant to study these systems ...dynamic systems with impulse effects has been ... See full document

... stochastic systems with Markovian switching is a class of hybrid dynamical systems, which is com- posed of both the logical switching rule of continuous-time finite-state Markovian process and the state ... See full document

... that stability is the major issue of control ...investigating stability. Razumikhin developed this technique to study the stability of deterministic systems with delay in [5] [6], then, Mao ... See full document

... hand, impulsive differential equations thrive to be a promising area and gained much attention among the researchers due to its potential application in various fields such as orbital transfer of satellite ... See full document

... the systems with time delay have received major attention in recent ...the systems with infinite delay deserve study because they portray a type of system existing in the real world [1-3,8] ...consider ... See full document

... some criteria on robust exponential stability by using the formula for the variation of parameters and estimating the Cauchy ...robust stability criteria do not require the stability of ... See full document

... random impulsive equations gives more realistic than deterministic impulsive ...random impulsive ordinary differential equations and investigated boundedness of soloutions to these models by ... See full document

... with impulsive effect provide mathematical models for many phenomena and processes in the field of natural sciences and ...developed stability theory of functional differential systems ... See full document

... nonlinear impulsive delay differential inequality is established, which can be applied in the dynamical analysis of nonlinear systems to improve many extant ...exponential stability of ... See full document

... The paper is organized as follows. In Section 1, introduction of preliminaries def- initions and notions which will be used in this paper. In Section 2, we introduce the notion of eventual stability of ... See full document

... Since impulsive dynamic equations with ‘slight vibration’ can be established on almost periodic time scales and describe many natural phenomena precisely, we propose a new type of ε-equivalent impulsive ... See full document

... Remark 3.2 As we pointed out in Introduction, to get the almost periodic solutions of impulsive differential equations, most people use the Contraction theorem. To be different, we use Schauder’s fixed ... See full document

... This paper studies the properties of solutions to system (1.1) by using the theory of func- tional differential equation, fractional differential equation, and stochastic analysis tech- niques. Firstly, we investigate the ... See full document

... fractional differential equations (FDE’s) have gained considerably more attention and attracted by many researchers in fields of such as physics, mechanics, chemistry, aerodynamics and the electrodynamics of ... See full document

... chosen. Stability in the Lyapunov sense (a special case of which is exponential stability) is a widely used definition in the control com- munity originating from the concept of ”energy” proposed by the ... See full document

... asymptotical stability of Runge-Kutta methods for a class of linear impulsive differential equations with piecewise continuous ...asymptotical stability region of Runge-Kutta methods for these ... See full document

... on impulsive control theory and Lyapunov method, we shall try to propose a new and practical impulsive strategy to realize the synchronization for a class of chaotic systems in Section ... See full document

... Several authors have studied the existence of solutions of abstract nonlinear impulsive evolution equations in Banach space[1, 3, 5, 6, 9, 10, 11, 12, 15, 16, 20, 21], D.J.Guo, V.Lakshimikantham and X.Z.Liu [5] ... See full document

... In the current paper, we are focused to study on some sufficient conditions for the existence results for abstract Cauchy problem for a class of mixed type impulsive fractional differential equations ... See full document

... In the future, we will concentrate all our efforts on other properties of this kind of equation discussed in our paper, such as on the existence of extremal solutions for SSDEs (2.2). Beside that, set-valued stochastic ... See full document