LMI-based transfer control for coexisting attractors in piecewise linear system

LI Deyang1,2, WU Shaopei2, LI Guofang2, DING Wangcai2, DING Jie2, YU Liyang2, WEI Xiaojuan3

Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (19) : 30-39.

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (19) : 30-39.

LMI-based transfer control for coexisting attractors in piecewise linear system

  • LI Deyang1,2, WU Shaopei2, LI Guofang2, DING Wangcai2, DING Jie2, YU Liyang2, WEI Xiaojuan3
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Abstract

The linear matrix inequality (LMI) and linear feedback method are used to migration the attractor under the guidance of the desired target orbit in a class of a two-degree-of-freedom piecewise-linearity system with clearance. Firstly, the coexisting attractors are identified on the state plane by cell mapping method. Meanwhile, the stability and transition mechanism of the coexisting attractors are studied based on Poincaré mapping and Lyapunov exponent. Secondly, according to the linear matrix inequality and Lyapunov theory, the stability of linear feedback control and the solution for feedback gain matrix are transformed into LMI description via the vector field information and s-procedure. Finally, the linear feedback controller and its gain matrix selection method are validated by numerical simulation.

Key words

Piecewise-linearity System / coexistent attractor / The linear matrix inequality / Attractor migration control

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LI Deyang1,2, WU Shaopei2, LI Guofang2, DING Wangcai2, DING Jie2, YU Liyang2, WEI Xiaojuan3. LMI-based transfer control for coexisting attractors in piecewise linear system[J]. Journal of Vibration and Shock, 2023, 42(19): 30-39

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