Impulsive synchronization of drive-response networks under adaptive quadratic feedback control
[Objective]The research of impulsive synchronization in complex networks has obtained abundant achievements,but there are few results on impulsive synchronization in drive-response complex networks driven by adaptive quadratic feedback control.Compared to the results of conventional impulsive synchronization,the control efficiency is better improved by designing a new adaptive secondary feedback controller.[Methods]In this paper,the Lyapunov function,the parameterization of ellipsoid boundary points and the theorem of impulse differential are applied to study the impulsive synchronization problem of time-delay and non-time-delay drive-response complex networks.[Results]With the adaptive quadratic feedback controller and adaptive law designed in this paper,By two theorems we can conclude that the error system is asymptotically stable in both time-delay and non-time-delay cases such that the trajectories of drive-response complex networks do not run out of the ellipsoid and are synchronized within the ellipsoidε((P))={e ∈Rn2:eT(P)e ≤ 1 }.We provide a framework for dealing with complex network synchronization problems with both quadratic terms and impulsive control.Finally,taking the single energy system as the nodes of the networks,a numerical example is given to verify the effectiveness and feasibility of the obtained results.[Conclusions]We can see that the system reaches synchronization faster with adaptive impulsive control containing a quadratic term.
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