Page 482 - Mathematical Techniques of Fractional Order Systems

468 Mathematical Techniques of Fractional Order Systems

respectively. From the results presented, it could be observed that synchroni-
zation was achieved by the convergence of the trajectories of the systems
and error state variables to zero. Fast and exponential convergence of the
error could be observed in all the different switches. The proposed control-
lers, by virtue of the convergence, could be said to be effective. By applying
the proposed controllers in this work added complexity, which translates to
better security will be introduced into the communication system. The multi-
switching component in this work can be used as a prearranged key in a
secure communication system.

15.6 CONCLUSION

The multiswitching synchronization of two fractional order chaotic systems
with different dimensions have been implemented using the method of active
controls. Six possible switches were proposed and controllers designed for
each of the six switches. Numerical simulations were carried out to test the
effectiveness of the proposed controllers. From the results presented, the con-
trollers were found to be effective by the convergence of the error dynamics
to zero.
However, there is the opportunity for further studies. Practical implemen-
tation of the proposed controllers using electronic simulation is hereby
recommended. Also recommended is the implementation of multiswitching
combination and combinaiton combination synchronization of fractional
order system with different dimensions. In particular, multiswitching syn-
chronization of two-, three-, and four-dimensional fractional order systems is
proposed.

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