The synchronizing methods are then compared from various point of views including synchronizing error variance, convergence time, control effort, maximum and minimum values of the control signal.
The simulation results are given in Figure 5. Figure 5 The synchronized error (pmb{Vert e_{i}(t) Vert _{2}}), (pmb{i=1,2,3,4,5,6}), of system ( 33 ) under pinning control ( 18 ).
The TTS halves the synchronization hops and effectively reduces the multi-hop synchronization error by synchronizing nodes of two adjacent levels.
In this article, we assume that all RSs in a cell can synchronize their transmissions perfectly, so that synchronization errors are negligible.
With nonzero initial conditions, the error system (2.6) is adaptively exponentially synchronized if the synchronization error satisfies (2.7).
As shown in Figure 3, the synchronization errors ({e_{i}}(t)) ((1 le i le100)) tend to synchronize in finite time.
Yet, in our system model, we assume that the elements of the antenna array are perfectly synchronized or that the synchronization error is small compared to the symbol length.
In contrast to the SES procedure, where all nodes are forced to synchronize in strict time intervals following a pattern (see Figure2), in the HIPESYN scheme any node is able to synchronize to any neighbor node when the synchronization error between both exceeds a fixed threshold, that is, when they really need to synchronize.
In Figure 2, the projective synchronization error system converges to zero, which shows that the drive and response systems are globally asymptotically projectively synchronized.
In addition, driving and driven trajectories are seen robustly synchronized with negligible errors in spite of the infliction of high frequency noise.
