文档介绍：
Robust Hybrid Projective Synchronization of
Fractional-Order Chaotic Systems with Time-Delay#
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MA Tiedong, XI Quan*
(College of Automation, Chongqing University, Chongqing 400044)
Abstract: The hybrid projective synchronization for fractional-order chaotic systems with time-delay
and uncertain perturbation is investigated in this paper. Adaptive sliding mode control method is
proposed to synchronize the fractional-order chaotic and hyperchaotic systems under time-delay and
uncertain perturbation. Stability is analyzed by using stability theorem of fractional calculus. The
simulation results show the feasibility and effectiveness of the proposed scheme.
Key words: Adaptive sliding mode control; Fractional-order systems; Hybrid projective
synchronization; Chaos
0 Introduction
The fractional differential calculus dates from 17th century which has almost the same long
history as integer calculus. Even though it has more than 300-year-old history, the fractional
calculus is primarily a pure theoretical field of mathematics and its application to physics and
engineering only develops in the recent years. Compared with the integer order model, fractional
calculus deals with derivatives and integration of arbitrary order and has deeper and more natural
connections with many fields of applied mathematics, engineering and physics. It has been found
that many systems in interdisciplinary fields can be described by fractional differential equations,
such as viscoelastic systems [1], dielectric polarization [2], electrode-electrolyte polarization [3],
quantitative finance [4], ic waves [5].
Recently, the control and synchronization of the fractional-order chaotic systems has e
an active topic for research due to its potential applications in munication and control
processing. Many researchers have made great contribution [6-17]. Amongst all kinds of chaos
synchronization, projective synchronization has been extensively investigat