The rich dynamics of fractional-order gyros applying a fractional controller

The gyro is an interesting and everlasting nonlinear nonautonomous dynamical system that exhibits very rich and complex behavior such as chaos. However, in recent years, modeling and control of fractional-order dynamical systems have become important and useful topics in both research and engineering applications. In this article, the dynamical behavior of a nonautonomous fractional-order gyro system is investigated. We apply the maximal Lyapunov exponent criterion to show that the fractional-order gyro system exhibits chaos. Strange attractors of the system are also plotted to validate the chaotic behavior of the system. Subsequently, in order to suppress the chaotic state of the fractional-order gyro system, a robust finite-time fractional controller is designed. The convergence time of the proposed control scheme is estimated. And the fractional Lyapunov theory is adopted to prove the finite-time stability and robustness of the proposed method. Besides, some computer simulations are given to illustrate the effectiveness and applicability of the proposed fractional controller.