Abstract
This letter further improves and extends the work of Kemih et al. In detail, feedback passivity synchronization with only one controller for a unified chaotic system is discussed here. It is noticed that the unified system contains the noted Lorenz, Lu, and Chen systems. Numerical simulations are given to show the effectiveness of these methods.
Highlights
Chaotic systems are characterized by being extremely sensitive to initial conditions, deterministically random, and unpredictable
We have shown that the passivity-based synchronization can be used to synchronize unified chaotic system
Numerical simulations given show the effectiveness of these methods
Summary
Chaotic systems are characterized by being extremely sensitive to initial conditions, deterministically random, and unpredictable. The character of passive system is one of the network theory concepts, which show characteristics of dissipative network. Passive network theory can be used to analyze the dynamical character of system, such as stabilization and dynamic characteristics. Our aim is to synchronize two unified chaotic systems. To achieve this goal, passive control theory is used to study passive synchronization of two unified chaotic systems. In the stable control region, the error dynamical system is transformed to a passive system, and using the state feedback, the error dynamical system can be globally asymptotically stabilized at zero. Some simulation results are provided for illustration and verification
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