[81] Daniel Liberzon. *Calculus of variations and optimal control theory. A concise introduction.*
Princeton, NJ: Princeton University Press, 2012.

[82] Jacques-Louis Lions and Enrico Magenes. *Non-Homogeneous Boundary Value Problems and Applications*. Springer Berlin Heidelberg, 1972.

[83] Yuning Liu, Takéo Takahashi, and Marius Tucsnak. Single input controllability of a simplified fluid-structure interaction model. *ESAIM Control Optim. Calc. Var.*, 19(1):20–42, 2013.

[84] Vladimir Logvinenko and Ju Sereda. Equivalent norms in spaces of entire functions of exponential type. *Teor. FunkciFunkcional. Anal. i Prilozen. Vyp*, 20:102–111, 1974.

[85] Frédéric Marbach. An obstruction to small-time local null controllability for a viscous Burgers' equation. In *Annales scientifiques de l'École Normale Supérieure*, volume 51(5), pages 1129–1177, 2018.

[86] Lawrence Markus. Controllability of nonlinear processes. *Journal of the Society for Industrial and Applied Mathematics, Series A: Control*, 3(1):78–90, 1965.

[87] Sorin Micu and Takéo Takahashi. Local controllability to stationary trajectories of a Burgers equation with nonlocal viscosity. *J. Differ. Equations*, 264(5):3664–3703, 2018.

[88] Luc Miller. On the controllability of anomalous diffusions generated by the fractional Laplacian. *Math. Control Signals Syst.*, 18(3):260–271, 2006.

[89] Luc Miller. A direct Lebeau-Robbiano strategy for the observability of heat-like semigroups. *Discrete Contin. Dyn. Syst., Ser. B*, 14(4):1465–1485, 2010.

[90] Andrii Mironchenko and Christophe Prieur. Input-to-state stability of infinite-dimensional systems: recent results and open questions. *SIAM Rev.*, 62(3):529–614, 2020.

[91] Fedor Nazarov. Local estimates for exponential polynomials and their applications to inequalities of the uncertainty principle type. *Algebra i Analiz*, 5(4):3–66, 1993.

[92] Albert Nijenhuis. Strong derivatives and inverse mappings. *Am. Math. Mon.*, 81:969–980, 1974.

[93] Jingrui Niu and Shengquan Xiang. Small-time local controllability of a KdV system for all critical lengths. *arXiv:2501.13640*, 2025.

[94] Amnon Pazy. *Semigroups of linear operators and applications to partial differential equations*, volume 44 of *Applied Mathematical Sciences*. Springer-Verlag, New York, 1983.

[95] Ramamurti Rajaraman. *Solitons and instantons: An introduction to solitons and instantons in quantum field theory*. North-Holland Personal Library, 1987.

[96] Jean-Pierre Raymond. Optimal control of partial differential equations, 2006.

[97] Eugène Remes. Sur une propriété extrémale des polynômes de Tchébychef. *Commun. Inst. Sci. math. méc. Univ. Kharkoff*, 4(13):93–95, 1936.

[98] Luc Robbiano. Cost function and control of solutions of hyperbolic equations. *Asymptotic Anal.*, 10(2):95–115, 1995.

[99] Lionel Rosier. Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain. *ESAIM, Control Optim. Calc. Var.*, 2:33–55, 1997.

[100] David Russell. Nonharmonic Fourier series in the control theory of distributed parameter systems. *J. Math. Anal. Appl.*, 18:542–560, 1967.
[101] David Russell. A unified boundary controllability theory for hyperbolic and parabolic partial differential equations. *Stud. Appl. Math.*, 52:189-211, 1973.

[102] Dietmar Salamon. Realization theory in Hilbert space. *Math. Syst. Theory*, 21(3):147-164, 1988.

[103] Helmut Schaefer. Über die Methode der a priori-Schranken. *Math. Ann.*, 129:415-416, 1955.

[104] Eric Schechter. *Handbook of analysis and its foundations*. San Diego, CA: Academic Press, 1997.

[105] Thomas Seidman. Two results on exact boundary control of parabolic equations. *Appl. Math. Optim.*, 11:145-152, 1984.

[106] Thomas Seidman. How violent are fast controls? *Math. Control Signals Systems*, 1(1):89-95, 1988.

[107] Thomas Seidman and Jiongmin Yong. How violent are fast controls? II. *Math. Control Signals Systems*, 9(4):327-340, 1996.

[108] Jacques Simon. Compact sets in the space $L^p(0, T; B)$. *Ann. Mat. Pura Appl. (4)*, 146:65-96, 1987.

[109] Eduardo Sontag. *Mathematical control theory*, volume 6 of *Texts in Applied Mathematics*. Springer-Verlag, New York, second edition, 1998. Deterministic finite-dimensional systems.

[110] Olof Johan Staffans. *Well-posed linear systems*, volume 103 of *Encycl. Math. Appl*. Cambridge: Cambridge University Press, 2005.

[111] Gianna Stefani. On the local controllability of a scalar-input control system. In *Theory and applications of nonlinear control systems (Stockholm, 1985)*, pages 167-179. North-Holland, Amsterdam, 1986.

[112] Héctor Sussmann. Lie brackets and local controllability: a sufficient condition for scalar-input systems. *SIAM J. Control Optim.*, 21(5):686-713, 1983.

[113] Héctor Sussmann. A general theorem on local controllability. *SIAM J. Control Optim.*, 25(1):158-194, 1987.

[114] Gérald Tenenbaum and Marius Tucsnak. On the null-controllability of diffusion equations. *ESAIM, Control Optim. Calc. Var.*, 17(4):1088-1100, 2011.

[115] Gérald Tenenbaum and Marius Tucsnak. New blow-up rates for fast controls of Schrödinger and heat equations. *J. Differ. Equations*, 243(1):70-100, 2007.

[116] Marius Tucsnak and George Weiss. *Observation and control for operator semigroups*. Birkhäuser Adv. Texts, Basler Lehrbüch. Basel: Birkhäuser, 2009.

[117] Marius Tucsnak and George Weiss. Well-posed systems – the LTI case and beyond. *Automatica*, 50(7):1757-1779, 2014.

[118] Pál Turán. On a theorem of Littlewood. *J. Lond. Math. Soc.*, 21:268-275, 1947.

[119] Jan van Neerven. Null controllability and the algebraic Riccati equation in Banach spaces. *SIAM J. Control Optim.*, 43(4):1313-1327, 2005.

[120] Gengsheng Wang, Ming Wang, Can Zhang, and Yubiao Zhang. Observable set, observability, interpolation inequality and spectral inequality for the heat equation in $\mathbb{R}^n$. *J. Math. Pures Appl. (9)*, 126:144-194, 2019.
[121] George Weiss. Admissibility of unbounded control operators. *SIAM J. Control Optim.*, 27(3):527-545, 1989.

[122] George Weiss. Representation of shift-invariant operators on $L^2$ by $H^\infty$ transfer functions: An elementary proof, a generalization to $L^p$, and a counterexample for $L^\infty$. *Math. Control Signals Syst.*, 4(2):193-203, 1991.

[123] Gerald Whitham. *Linear and nonlinear waves*. Pure Appl. Math., Wiley-Intersci. Ser. Texts Monogr. Tracts. New York, NY: Wiley, paperback ed. edition, 1999.

[124] Yubiao Zhang. Unique continuation estimates for the Kolmogorov equation in the whole space. *C. R., Math., Acad. Sci. Paris*, 354(4):389-393, 2016.

[125] Enrique Zuazua. Exact controllability for semilinear wave equations in one space dimension. *Ann. Inst. Henri Poincaré, Anal. Non Linéaire*, 10(1):109-129, 1993.