References
- Sriram K, Gopinathan MS. A two variable delay model for the circadian rhythm of Neurospora crassa. J. Theor. Biol. 2004;231:23–38.
- Srividhya J, Gopinathan MS. A simple time delay model for eukaryotic cell cycle. J. Theor. Biol. 2006;241:617–627.
- Datko R, Lagnese J, Polis M. An example on the effect of time delays in boundary feedback stabilization of wave equations. SIAM J. Control Optim. 1986;24:152–156.
- Datko R. Two examples of ill-posedness with respect to small delays in stabilized elastic systems. IEEE Trans. Automat. Control. 1993;38:163–166.
- Datko R, You YC. Some second-order vibrating systems cannot tolerate small time delays in their damping. J. Optimiz. Theory Appl. 1991;70:521–537.
- Machtyngier E. Exact controllability for the Schrödinger equation. SIAM J. Control Optim. 1994;32:24–34.
- Machtyngier E, Zuazua E. Stabilization of the Schrödinger equation. Port. Math. 1994;51:243–256.
- Liu JJ, Wang JM. Output-feedback stabilization of an anti-stable Schrödinger equation by boundary feedback with only displacement observation. J. Dyn. Control Syst. 2013;19:471–482.
- Bortot CA, Cavalcanti MM, Correa WJ, Domingos VN. Cavalcanti, Uniform decay rate estimates for Schrödinger and plate equations with nonlinear locally distributed damping. J. Differ. Equ. 2013;254:3729–3764.
- Guo BG, 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. 2014;24:2194–2212.
- Wen RL, Chai SG, Guo BZ. Well-Posedness and exact controllability of fourth order Schrödinger equation with boundary control and collocated observation. SIAM J. Control Optim. 2014;52:365–396.
- Ren BB, Wang JM, Krstic M. Stabilization of an ODE-Schrödinger cascade. Syst. Control Lett. 2013;62:503–510.
- Mörgul O. On the stabilization and stability robustness against small delays of some damped wave equation. IEEE Trans. Automat. Control. 1995;40:1626–1630.
- Guo BZ, Xu CZ, Hammouri H. Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary obserbation. ESAIM: Control Optim. Calc. Var. 2012;18:22–35.
- Guo BZ, Yang KY. Output feedback stabilization of a one-dimensional Schrödinger equation by boundary observation with time delay. IEEE Trans. Automat. Control. 2010;55:1226–1232.
- Yang KY, Yao CZ. Stabilization of one-dimensional Schrödinger equation with variable coefficient under delayed boundary output. Asian J. Control. 2013;15:1531–1537.
- Kafini M, Messaoudi SA, Mustafa MI. Energy decay rates for a Timoshenko-type system of thermoelasticity of type III with constant delay. Appl. Anal. 2014;93:1201–1216.
- Nicaise S, Pignotti C. Stabilization of second-order evolution equations with time delay. Math. Control Signals Syst. 2014;26:563–588.
- Nicaise S, Valein J. Stabilization of second order evolution equations with unbounded feedback with delay, ESAIM: Control Optim. Calc. Var. 2010;16:420–456.
- Nicaise S, Rebiai S. Stability of the Schrödinger equation with a delay term in the boundary or internal feedbacks. Port. Math. 2011;68:19–39.
- Xu GQ, Yung SP, Li LK. Stabilization of wave systems with input delay in the boundary control. ESAIM: Control Optim. Calc. Var. 2006;12:770–785.
- Han ZJ, Xu GQ. Exponential stability of Timoshenko beam system with delay terms in boundary feedbacks. ESAIM: Control Optim. Calc. Var. 2011;17:552–574.
- Han ZJ, Xu GQ. Dynamical behavior of networks of non-uniform Timoshenko beams system with boundary time-delay inputs. Netw. Heterog. Media. 2011;6:297–327.
- Ait Benhassi EM, Ammari K, Boulite S, Maniar L. Feedback stabilization of a class of evolution equations with delay. J. Evol. Equ. 2009;9:103–121.
- Said-Houari B, Laskri Y. A stability result of a Timoshenko system with a delay term in the internal feedback. Appl. Math. Comput. 2010;217:2857–2869.
- Krstic M, Guo BZ, Smyshlyaev A. Boundary controllers and observers for the linearized Schrödinger equation. SIAM J. Control Optim. 2011;49:1479–1497.
- Shang YF, Xu GQ. Stabilization of Euler–Bernoulli beam with input delay in the boundary control. Syst. Control Lett. 2012;61:1069–1078.
- Shang YF, Xu GQ. Output-based stabilization for a one-dimensional wave equation with distributed input delay in the boundary control. IMA J. Math. Control Info. Forthcoming. doi:10.1093/imamci/dnu030.
- Pazy A. Semigroup of linear operator and applications to partial differential equations. Berlin: Springer-Verlag; 1983.
- Tucsnak M, Weiss G. Observation and control for operator semigroups. Basel: Birkhaüser; 2009.