Abstract
This paper presents the robust synchronization problem of a 3D chaotic system by using the active control technique. Based on the Gershgorin theorem and Routh-Hurwitz criterion, sufficient algebraic conditions are derived to design a linear controller gain matrix. The conditions are then applied for the robust stability of the synchronization error dynamics in the presence of an unknown bounded smooth external disturbance. The proposed active control strategy with a suitable computation of the linear controller gain matrix is simple in design and establishes fast convergence rates of the synchronization error signals. Numerical simulation results further verified the analytical results.
Highlights
For the last two decades, chaos synchronization has been widely explored in various research fields [1,2,3]
Using the active control algorithm, Agiza and Yaseen [13] presented the synchronization of two identical Rossler and two identical Chen chaotic systems
Lei et al [14] reported the synchronization problem of two identical nonlinear gyros using the active control based on the Routh-Hurwitz criterion and Lyapunov stability theory
Summary
For the last two decades, chaos synchronization has been widely explored in various research fields [1,2,3]. Lei et al [14] reported the synchronization problem of two identical nonlinear gyros using the active control based on the Routh-Hurwitz criterion and Lyapunov stability theory. Ahmad et al [10], addressed the synchronization problem of two identical and two non-identical chaotic systems using the active control technique based on the Lyapunov stability theory. In this article, based on the Gershgorin theorem [19] and Routh-Hurwitz criterion [20] and using the active control strategy, a generalized approach is proposed to compute a suitable linear controller gain matrix that establishes globally asymptotical synchronization under the effect of unknown external disturbance. The rest of the paper is organized as follows: In Section 2, the problem statement is given and derived the generic criterion to construct a proper linear control gain matrix using the active control technique.
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