Synchronization of coupled memristive chaotic circuits via state-dependent impulsive control
This paper investigates the synchronization of two memristive chaotic circuits via state-dependent impulsive control. Different from most existing publications, impulses occurring is not at fixed instants but depends on the states of systems. Furthermore, the state variables of the driving system (d...
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| Published in: | Nonlinear dynamics 2017-04, Vol.88 (1), p.115-129 |
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Synchronization of coupled memristive chaotic circuits via state-dependent impulsive control |
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Yang, Shiju Li, Chuandong Huang, Tingwen |
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Automotive Engineering Circuits Classical Mechanics Computer simulation Control Differential equations Dynamical Systems Economic models Engineering Impulses Mechanical Engineering Original Paper State variable Synchronism Vibration |
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Nonlinear dynamics, 2017-04, Vol.88 (1), p.115-129 |
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This paper investigates the synchronization of two memristive chaotic circuits via state-dependent impulsive control. Different from most existing publications, impulses occurring is not at fixed instants but depends on the states of systems. Furthermore, the state variables of the driving system (driving system which does not involve the impulses) are transmitted to the response system, and then the state variables of response system are subjected to jumps at the state-dependent impulsive instants, and ultimately to achieve synchronization. Based on the Lyapunov stability theory, impulsive differential equation, and inequality techniques, the sufficient conditions with theoretical demonstration ensuring every solution of error system intersects each surface of the discontinuity exactly once are derived. Then, by applying B-equivalence method, the error system with state-dependent impulses can be reduced to the case of fixed-time impulses. Finally, the numerical simulations are carried out to demonstrate the effectiveness of the obtained results. |
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Different from most existing publications, impulses occurring is not at fixed instants but depends on the states of systems. Furthermore, the state variables of the driving system (driving system which does not involve the impulses) are transmitted to the response system, and then the state variables of response system are subjected to jumps at the state-dependent impulsive instants, and ultimately to achieve synchronization. Based on the Lyapunov stability theory, impulsive differential equation, and inequality techniques, the sufficient conditions with theoretical demonstration ensuring every solution of error system intersects each surface of the discontinuity exactly once are derived. Then, by applying B-equivalence method, the error system with state-dependent impulses can be reduced to the case of fixed-time impulses. 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