Exponential Synchronizationlike Criterion for State-Dependent Impulsive Dynamical Networks

Abstract

This paper focuses on the problem of the exponential synchronizationlike criteria for state-dependent impulsive dynamical networks (SIDNs). Two types of sufficient conditions, which are applied to ensure every solution intersecting each impulsive surface exactly once, are derived. For each type of collision conditions, combining with comparison principle and inequality techniques, some sufficient conditions are obtained to ensure local exponential synchronizationlike for SIDN. Moreover, a quiet different impulsive strategy concerning the trigger rules of impulsive instants is proposed. Finally, an example is given to demonstrate the effectiveness of our results.

Robust exponential stabilization of stochastic coupled T‐S fuzzy complex networks subject to state‐dependent impulsive control

“…In addition, research on the state‐dependent impulse has also become an important topic 20‐29 . Due to the complexity of theoretical analysis, many traditional methods of analysis are no longer applicable, the main effective approaches are mainly divided two part: B‐equivalent method (main analysis approach) 20‐26 and impulse time window method 27‐29 . In this paper, one of the most difficult problems is the beating phenomena which is induced by a solution intersecting one impulsive surface many times.…”

“…In addition, research on the state-dependent impulse has also become an important topic. [20][21][22][23][24][25][26][27][28][29] Due to the complexity of theoretical analysis, many traditional methods of analysis are no longer applicable, the main effective approaches are mainly divided two part: B-equivalent method (main analysis approach) [20][21][22][23][24][25][26] and impulse time window method. [27][28][29] In this paper, one of the most difficult problems is the beating phenomena which is induced by a solution intersecting one impulsive surface many times.…”

“…22,24 Besides, Song et al 23 extended the B-equivalent method to the fractional-order time-varying impulsive system. Li et al 21 improved the B-equivalent method and reduced the conservatism of the obtained conditions.…”

Stability for a Class of State Constrained Impulsive Nonlinear Systems: Barrier Lyapunov Functions Method

“…A system in which the state suddenly changes at some moment cannot be described as a single continuous dynamical system or a discretetime dynamical system, so it is natural that people put forward an impulsive system to describe the dynamic system with impulsive phenomenon. In recent decades, many researchers have focused on stability or control of impulsive systems or hybrid systems, include Lyapunov stability of impulsive systems [8][9][10][11][12], impulsive control for synchronization of complex networks [13], application of hybrid systems [14,15]. Impulsive systems have been studied for a long time, but still less referred to the state constrained impulsive nonlinear systems.…”

Fully relative state constraint impulsive consensus of nonlinear multi‐agent systems via state‐dependent impulsive protocols

“…In addition, fixed-time impulsive protocols require the design of the impulsive interval before the systems commence, but for application we often need to chose variable instants in limit time intervals. Compared with the limitation of fixed-time impulses, variable-time impulses where the jump moments of impulses depend on the states are more practical and valuable [31][32][33], such as population control system, fishing control system, energy conservation system and so on. However, there exist a lot of difficulties to analyse system with variable-time impulses because of the uncertain impulsive instants and beating phenomena.…”