Stabilization for a cable with tip mass under boundary input disturbance

References

• Morgul O, Rao B, Conrad F. On the stabilization of a cable with a tip mass. IEEE Trans Automat Control. 1994;39(10):2140–2145.
   Web of Science ®Google Scholar
• Guo BZ, Xu CZ. On the spectrum-determined growth condition of a vibration cable with a tip mass. IEEE Trans Automat Control. 2000;45(1):89–93.
   Web of Science ®Google Scholar
• Lee EB, You YC. Stabilization of a hybrid (string/point mass) system. In: Proceedings of 5th International Conference on Systems Engineering. Dayton, OH, 1987.
   Google Scholar
• Lee EB, You YC. Stabilization of a vibrating string system linked by point masses. In: Control of boundaries and stabilization, 1989. p. 177–198. (Lecture notes in Control and Inform. Sci.; 125).
   Google Scholar
• Hansen S, Zuazua E. Controllability and stabilization of strings with point masses. SIAM J Cont Optim. 1995;33(5):1357–1391.
   Web of Science ®Google Scholar
• Chen YL, Han ZJ, Xu GQ, et al. Exponential stability of string system with variable coefficients under non-collocated feedback controls. Asian J Control. 2011;13(1):148–163.
   Web of Science ®Google Scholar
• Chen G, Delfour M, Krall AM, et al. Modelling, stabilization and control of serially connected beams. SIAM J Control Optim. 1987;25(3):526–546.
   Web of Science ®Google Scholar
• Littman W, Markus L. Exact boundary controllability of a hybrid system of elasticity. Arch Rational Mech Anal. 1988;103(3):193–236.
   Web of Science ®Google Scholar
• Littman W, Markus L. Stabilization of a hybrid system of elasticity by feedback boundary damping. Annali di Matematica Pura ed Applicata. 1988;152(1):281–330.
   Web of Science ®Google Scholar
• Chen X, Chentouf B, Wang JM. Exponential stability of a non-homogeneous rotating disk-beam-mass system. J Math Anal Appl. 2015;423(2):1243–1261.
   Web of Science ®Google Scholar
• Orlov Y, Utkin VI. Unit sliding mode control in infinite-dimensional systems. Appl Math Comput Sci. 1998;8(1):7–20.
   Google Scholar
• Guo BZ, Jin FF. Sliding mode and active disturbance rejection control to stabilization of one-dimensional anti-stable wave equations subject to disturbance in boundary input. IEEE Trans Automat Control. 2013;58(5):1269–1274.
   Web of Science ®Google Scholar
• Guo BZ, Zhou HC, AL-Fhaid AS, et al. Stabilization of Euler-Bernoulli beam equation with boundary moment control and disturbance by active disturbance rejection control and sliding mode control approaches. J Dyn Control Syst. 2014;20(4):539–558.
   Web of Science ®Google Scholar
• Guo BZ, Liu JJ. 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. 2008;24(16):2194–2212.
   Web of Science ®Google Scholar
• Guo W, Guo BZ. Adaptive output feedback stabilization for one-dimensional wave equation with corrupted observation by harmonic disturbance. SIAM J Control Optim. 2013;51(2):1679–1706.
   Web of Science ®Google Scholar
• Ge SS, Zhang S, He W. Vibration control of an Euler–Bernoulli beam under unknown spatiotemporally varying disturbance. Int J Control. 2011;84(5):947–960.
   Web of Science ®Google Scholar
• Zhu QX. Stabilization of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control. IEEE Trans Automat Contr. 2019;64(9):3764–3771.
   Web of Science ®Google Scholar
• Wang H, Zhu QX. Adaptive output feedback control of stochastic nonholonomic systems with nonlinear parameterization. Automatica. 2018;98:247–255.
   Web of Science ®Google Scholar
• Orlov Y, Utkin VI. Sliding mode control in infinite-dimensional systems. Automatica. 1987;23(6):753–757.
   Web of Science ®Google Scholar
• Pazy A. Semigroups of linear operators and applications to partial differential equations. New York: Springer-Verlag; 1983.
   Google Scholar
• Barbu V. Nonlinear semigroups and differential equations in banach space. Leyden: Noordhoff; 1976.
   Google Scholar
• Xu GQ. Generalization of Lions-Lax-Milgram theorem and application to solvability of discontinuous differential equation. preprint.
   Google Scholar
• Xu GQ, Xu C. Stabilization of 1-d wave equation with input disturbance. preprint.
   Google Scholar
• Khalil HK. Nolinear system. New York: Prentice Hall; 2001.
   Google Scholar