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Figure 3 displays the synchronization errors between the master system (12) and the slave system (13) in 4D.
Obviously, Figure 3 indicates that we have achieved the synchronization between the master system (12) and the slave system (13).
Figure 3 Time series of the synchronized error signals between the master system ( 12 ) and the slave system ( 13 ) in 4D.
As can be seen in Figure 4, the synchronization occurs between the master system (12) and the slave system (24) in 3D. Figure 4 Time series of the synchronized error signals between the master system ( 12 ) and the slave system ( 24 ) in 3D. Figure 1 displays the chaotic attractor of three-dimensional autonomous system (1).
Remark 3 In this paper, a modified impulsive control system is adopted to provide the basis for developing global exponential synchronization between the master system and the slave system, which can reduce the impulsive times and the control cost effectively.
By using the Lyapunov functional method, some delay-dependent synchronization criteria in terms of linear matrix inequality are proposed to ensure the mean square synchronization between the master system and the slave system.
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Let e ( t ) = y ( t ) − x ( t ) be the synchronization error between the states of the master system (2.1) and the slave system (2.2).
The LMI condition guarantees that the synchronization between the slave system and the master system is achieved.
The aim is to design a suitable controller to achieve the projective synchronization between the slave system and the master system.
Then the master system becomes (2.9).
The system, which is called a slave system or a response system, can be driven by another system, which is called a master system or drive system, so that the behavior of the slave system can be influenced by the master system, i.e., the master system is independent to the slave system but the slave system is driven by the master system.
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