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Zbl 1156.34331
Yau, Her-Terng
Synchronization and anti-synchronization coexist in two-degree-of-freedom dissipative gyroscope with nonlinear inputs. (English)
[J] Nonlinear Anal., Real World Appl. 9, No. 5, 2253-2261 (2008). ISSN 1468-1218

Summary: This study demonstrates that synchronization and anti-synchronization can coexist in two-degree-of-freedom dissipative gyroscope system with input nonlinearity. Because of the nonlinear terms of the gyroscope system, the system exhibits complex motions containing regular and chaotic motions. Using the variable structure control technique, a novel control law is established which guarantees the hybrid projective synchronization including synchronization, anti-synchronization and projective synchronization even when the control input nonlinearity is present. By Lyapunov stability theory with control terms, two suitable sliding surfaces are proposed to ensure the stability of the controlled closed-loop system in sliding mode, and two variable structure controllers (VSC) are designed to guarantee the hitting of the sliding surfaces. Numerical simulations are presented to verify the proposed synchronization approach.

MSC 2000:: *34D20 Lyapunov stability of ODE
70K28 Parametric resonances
70E05 Motion of the gyroscope

Keywords: gyroscope; synchronization; anti-synchronization; chaos; input nonlinearity; variable structure control

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