The anti-disturbance property of a closed-loop system of 1-d wave equation with boundary control matched disturbance.

*(English)*Zbl 07144734Summary: We study the anti-disturbance problem of a 1-d wave equation with boundary control matched disturbance. In earlier literature, the authors always designed the controller such as the sliding mode control and the active disturbance rejection control to stabilize the system. However, most of the corresponding closed-loop systems are boundedly stable. In this paper we show that the linear feedback control also has a property of anti-disturbance, even if the disturbance includes some information of the system. By choosing suitable parameters introduced in the proof, we can ensure the solution of the closed-loop system is bounded in an admissible range. As an application, we discuss the control problem of a nonlinear system. As a result, it is shown that the bounded estimation of the solution is suitable.

##### MSC:

35B35 | Stability in context of PDEs |

93C05 | Linear systems in control theory |

93C20 | Control/observation systems governed by partial differential equations |

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\textit{X.-R. Wang} and \textit{G.-Q. Xu}, Appl. Math., Praha 64, No. 6, 695--714 (2019; Zbl 07144734)

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