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.
In particular, we show how to control the frequency of the synchronization episodes, and obtain a rigorous estimate for the simplest case.
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, 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.
Second, by employing the invariance principle of functional differential equations, a simple, analytical, and rigorous adaptive feedback scheme is proposed for the robust synchronization of almost all kinds of coupled neural networks with time-varying delay based on the parameter identification of uncertain delayed neural networks.
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.
