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**Finite-time stabilization of uncertain non-autonomous chaotic gyroscopes with nonlinear inputs.**
*(English)*
Zbl 1233.93081

Summary: Gyroscopes are one of the most interesting and everlasting nonlinear nonautonomous dynamical systems that exhibit very complex dynamical behavior such as chaos. In this paper, the problem of robust stabilization of the nonlinear non-autonomous gyroscopes in a given finite time is studied. It is assumed that the gyroscope system is perturbed by model uncertainties, external disturbances, and unknown parameters. Besides, the effects of input nonlinearities are taken into account. Appropriate adaptive laws are proposed to tackle the unknown parameters. Based on the adaptive laws and the finite-time control theory, discontinuous finite-time control laws are proposed to ensure the finite-time stability of the system. The finite-time stability and convergence of the closed-loop system are analytically proved. Some numerical simulations are presented to show the efficiency of the proposed finite-time control scheme and to validate the theoretical results.

### MSC:

93D21 | Adaptive or robust stabilization |

93C10 | Nonlinear systems in control theory |

93C40 | Adaptive control/observation systems |

34C28 | Complex behavior and chaotic systems of ordinary differential equations |

34H10 | Chaos control for problems involving ordinary differential equations |

37N35 | Dynamical systems in control |

70Q05 | Control of mechanical systems |

### Keywords:

nonlinear nonautonomous dynamical system; robust stabilization; model uncertainties; external disturbances; adaptive laws; finite-time stability; convergence of the closed-loop system
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\textit{M. P. Aghababa} and \textit{H. P. Aghababa}, Appl. Math. Mech., Engl. Ed. 33, No. 2, 155--164 (2012; Zbl 1233.93081)

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