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Universal stabilisation design for general non-linear systems under wave partial differential equation actuator dynamics with time-varying moving boundary

Universal stabilisation design for general non-linear systems under wave partial differential equation actuator dynamics with time-varying moving boundary

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A universal stabilisation formula is presented for globally (or locally) asymptotical stabilisation for general non-linear systems governed by wave actuator dynamics with time-varying moving boundary in this study. Stability analysis is developed with passivity-based synthesis approach and infinite-dimensional backstepping transformations. Under the backstepping transformations and the control law design, the original system is transferred to the target system. Then the authors prove that the target system is asymptotical stable. Moreover, it is shown that the stability of the original system is equivalent to that of the target system. Finally, three examples are given to illustrate the effectiveness of the proposed design technique.

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