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boundary control; disturbance; wave equation; anti-disturbance

References:

[1] Cox, S., Zuazua, E.: **The rate at which energy decays in a damped string**. Commun. Partial Differ. Equations 19 (1994), 213-143. DOI 10.1080/03605309408821015 | MR 1257004 | Zbl 0818.35072

[2] Fu, Q. H., Xu, G. Q.: **Exponential stabilization of 1-d wave equation with distributed disturbance**. WSEAS Trans. Math. 14 (2015), 192-201.

[3] Guo, W., Guo, B.-Z., Shao, Z.-C.: **Parameter estimation and stabilization for a wave equation with boundary output harmonic disturbance and non-collocated control**. Int. J. Robust Nonlinear Control 21 (2011), 1297-1321. DOI 10.1002/rnc.1650 | MR 2840009 | Zbl 1244.74038

[4] Guo, B.-Z., Jin, F.-F.: **The active disturbance rejection and sliding mode control approach to the stabilization of the Euler-Bernoulli beam equation with boundary input disturbance**. Automatica 49 (2013), 2911-2918. DOI 10.1016/j.automatica.2013.06.018 | MR 3084483 | Zbl 1364.93637

[5] Guo, B.-Z., Kang, W.: **The Lyapunov approach to boundary stabilization of an anti-stable one-dimensional wave equation with boundary disturbance**. Int. J. Robust Nonlinear Control 24 (2014), 54-69. DOI 10.1002/rnc.2874 | MR 3149286 | Zbl 1278.93199

[6] Guo, B.-Z., Liu, J.-J.: **Sliding mode control and active disturbance rejection control to the stabilization of one-dimensional Schrödinger equation subject to boundary control matched disturbance**. Int. J. Robust. Nonlinear Control 24 (2014), 2194-2212. DOI 10.1002/rnc.2977 | MR 3271988 | Zbl 1302.93060

[7] Guo, B.-Z., Liu, J.-J., Al-Fhaid, A. S., Mahmood, M. Arshad, Younas, A. M. M., Asiri, A.: **The active disturbance rejection control approach to stabilisation of coupled heat and ODE system subject to boundary control matched disturbance**. Int. J. Control 88 (2015), 1554-1564. DOI 10.1080/00207179.2015.1010179 | MR 3371068 | Zbl 1337.93078

[8] Guo, B.-Z., Zhou, H.-C.: **The active disturbance rejection control to stabilization for multi-dimensional wave equation with boundary control matched disturbance**. IEEE Trans. Autom. Control 60 (2015), 143-157. DOI 10.1109/TAC.2014.2335511 | MR 3299420 | Zbl 1360.93545

[9] Immonen, E., Pohjolainen, S.: **Feedback and feedforward output regulation of bounded uniformly continuous signals for infinite-dimensional systems**. SIAM J. Control Optim. 45 (2006), 1714-1735. DOI 10.1137/050623000 | MR 2272163 | Zbl 1127.93029

[10] Jayawardhana, B., Weiss, G.: **State convergence of passive nonlinear systems with an $L^2$ input**. IEEE Trans. Autom. Control 54 (2009), 1723-1727. DOI 10.1109/TAC.2009.2020661 | MR 2535777 | Zbl 1367.93435

[11] Jin, F.-F., Guo, B.-Z.: **Lyapunov approach to output feedback stabilization for the Euler-Bernoulli equation with boundary input disturbance**. Automatica 52 (2015), 95-102. DOI 10.1016/j.automatica.2014.10.123 | MR 3310818 | Zbl 1309.93122

[12] Ke, Z., Logemann, H., Rebarber, R.: **Approximate tracking and disturbance rejection for stable infinite-dimensional systems using sampled-data low-gain control**. SIAM J. Control Optim. 48 (2009), 641-671. DOI 10.1137/080716517 | MR 2486087 | Zbl 1194.93043

[13] Krstic, M.: **Adaptive control of an anti-stable wave PDE**. Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 17 (2010), 853-882. MR 2757916 | Zbl 1219.93055

[14] Nakao, M.: **Decay of solutions of the wave equation with a local nonlinear dissipation**. Math. Ann. 305 (1996), 403-417. DOI 10.1007/BF01444231 | MR 1397430 | Zbl 0856.35084

[15] Rebarber, R., Weiss, G.: **Internal model based tracking and disturbance rejection for stable well-posed systems**. Automatica 39 (2003), 1555-1569. DOI 10.1016/S0005-1098(03)00192-4 | MR 2143463 | Zbl 1028.93012

[16] Shang, Y., Xu, G.: **Dynamic control of an Euler-Bernoulli equation with time-delay and disturbance in the boundary control**. Int. J. Control 92 (2019), 27-41. DOI 10.1080/00207179.2017.1334264 | MR 3928477 | Zbl 1415.93117

[17] Weiss, G.: **Admissibility of unbounded control operators**. SIAM J. Control Optimization 27 (1989), 527-545. DOI 10.1137/0327028 | MR 0993285 | Zbl 0685.93043

[18] Xie, Y. R., Xu, G. Q.: **Stabilization of a wave equation with a tip mass based on disturbance observer of time-varying gain**. J. Dyn. Control Syst. 23 (2017), 667-677. DOI 10.1007/s10883-016-9349-0 | MR 3688888 | Zbl 1372.35175

[19] Xu, G. Q.: **Exponential stabilization of conservation systems with interior disturbance**. J. Math. Anal. Appl. 436 (2016), 764-781. DOI 10.1016/j.jmaa.2015.11.079 | MR 3446978 | Zbl 1330.93210

[20] Zhao, Z., Guo, B.: **Active disturbance rejection control to stabilize one-dimensional wave equation with interior domain anti-damping and boundary disturbance**. Control Theory Appl. 30 (2013), 1553-1563. DOI 10.7641/CTA.2013.30966 | Zbl 1299.93247