| Synchronization and control of chaotic systems have been a hot topic in nonlinearscience due to their potential applications in various fields. Base on the finite-time stabilitytheory and Gerschgorin disc theorem, finite-time synchronization of a class of autonomouschaotic systems, combination synchronization among three identical incommensuratefractional-order chaotic systems and finite-time combination-combination synchronization forhyperchaotic systems are investigated.Firstly, based on the finite-time stability theory, chaos synchronization of a class ofnth-order autonomous chaotic systems in a given finite time is investigated. Some sufficientcriteria for achieving the finite-time synchronization are derived by the Lyapunov directmethod and Gerschgorin disc theorem, respectively. Considering the property of similarmatrices, some more flexible criteria are obtained. Numerical simulations verify thefeasibility of the control strategy.Secondly, based on the idea of tracking control, two different controllers are designed toachieve the combination synchronization among three incommensurate fractional-order Lu systems. The designed controllers are given by using the stability theory of incommensuratefractional-order linear systems and the stability determinant theorem of fractional-orderchaotic systems, respectively. Numerical simulations illustrate the effectiveness of theproposed method.Finally, based on the finite-time stability theory, step-by-step control and nonlinearcontrol method, a suitable controller is designed to achieve finite-time combination-combination synchronization among four hyperchaotic systems. Numerical simulations verifythe effectiveness of the control strategy. |
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