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However, the system model considered in [13] was not practical which required the information to be perfectly exchanged with the inner of the cluster and rigorous synchronization for each user.
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Second, the method is frequency independent, in line with a rigorous mathematical definition of synchronization [22], [23].
The two schemes, based on the stability theory of the fractional-order system, are rather simple, theoretically rigorous and convenient to realize synchronization.
Rigorous proof shows that attitude synchronization of multiple spacecraft can be achieved in finite time, and the control scheme satisfies input saturation requirement.
By utilizing a new lemma on impulsive differential inequality and the Lyapunov functional method, several synchronization criteria are obtained through rigorous mathematical proofs.
In particular, we show how to control the frequency of the synchronization episodes, and obtain a rigorous estimate for the simplest case.
In particular, the approach developed in [15] has illustrated a rigorous study to prove the coexistence of some synchronization types between discrete-time chaotic (hyperchaotic) systems.
Rigorous proof shows that the systems output can reach synchronization in a finite time and the final consensus states are the leader׳s states.
The design of the synchronization framework followed well-established principles of rigorous software engineering.
This synchronization approach that is simple, global and theoretically rigorous enables synchronization of fractional-order chaotic systems be achieved in a systematic way and does not require the computation of the conditional Lyapunov exponents.
We have also investigated chaos synchronization between two coupled identical systems, from a rigorous mathematical approach.
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