Remarks on input-to-state stability of collocated systems with saturated feedback

Cazenave T, Haraux A (1998) An introduction to semilinear evolution equations, Oxford Lecture Series in Mathematics and its Applications, vol 13. The Clarendon Press, Oxford University Press, New York Curtain R, Zwart H (2020) Introduction to infinite-dimensional systems theory: a state-space approach, Texts in applied mathematics, vol 71. Springer, New York, NY Dashkovskiy S, Mironchenko A (2013) Input-to-state stability of infinite-dimensional control systems. Math Control Signals Syst 25(1):1–35 Engel KJ, Nagel R (2000) One-parameter semigroups for linear evolution equations, Graduate Texts in Mathematics, vol 194. Springer, New York. With contributions by S. Brendle, M. Campiti, T. Hahn, G. Metafune, G. Nickel, D. Pallara, C. Perazzoli, A. Rhandi, S. Romanelli and R. Schnaubelt Grüne L (1999) Input-to-state stability of exponentially stabilized semilinear control systems with inhomogeneous perturbations. Syst Control Lett 38(1):27–35 Guiver C, Logemann H (2020) A circle criterion for strong integral input-to-state stability. Automatica J IFAC 111:108641 Guiver C, Logemann H, Opmeer MR (2019) Infinite-dimensional Lur’e systems: input-to-state stability and convergence properties. SIAM J Control Optim 57(1):334–365 Jacob B, Mironchenko A, Partington JR, Wirth F (2019) Non-coercive Lyapunov functions for input-to-state stability of infinite-dimensional systems. arXiv: 1911.01327 Jacob B, Nabiullin R, Partington JR, Schwenninger F (2018) Infinite-dimensional input-to-state stability and Orlicz spaces. SIAM J Control Optim 56(2):868–889 Lasiecka I, Seidman T (2003) Strong stability of elastic control systems with dissipative saturating feedback. Syst Control Lett 48:243–252 Marx S, Andrieu V, Prieur C (2017) Cone-bounded feedback laws for \(m\)-dissipative operators on Hilbert spaces. Math Control Signals Syst 29(4), Art. 18, 32 Marx S, Cerpa E, Prieur C, Andrieu V (2015) Stabilization of a linear Korteweg-de Vries equation with a saturated internal control. In: 14th annual European Control Conference (ECC15). Linz, Austria Marx S, Cerpa E, Prieur C, Andrieu V (2016) Global stabilization of a Korteweg-de Vries equation with a distributed control saturated in \(L_2\)-norm. In: 10th IFAC symposium on nonlinear control systems (NOLCOS 2016). Monterey, CA, USA Marx S, Cerpa E, Prieur C, Andrieu V (2017) Global stabilization of a Korteweg-de Vries equation with saturating distributed control. SIAM J Control Optim 55(3):1452–1480 Marx S, Chitour Y, Prieur C (2018) Stability results for infinite-dimensional linear control systems subject to saturations. In: 16th European control conference (ECC 2018). Limassol, Cyprus Marx S, Chitour Y, Prieur C (2020) Stability analysis of dissipative systems subject to nonlinear damping via lyapunov techniques. IEEE Trans Autom Control 65(5):2139–2146 Mironchenko A (2016) Local input-to-state stability: characterizations and counterexamples. Syst Control Lett 87:23–28 Mironchenko A, Prieur C (2019) Input-to-state stability of infinite-dimensional systems: recent results and open questions. arXiv: 1910.01714 Mironchenko A, Wirth F (2018) Characterizations of input-to-state stability for infinite-dimensional systems. IEEE Trans Automat Control 63(6):1602–1617 Mironchenko A, Wirth F (2018) Lyapunov characterization of input-to-state stability for semilinear control systems over Banach spaces. Syst Control Lett 119:64–70 Pazy A (1983) Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, vol 44. Springer, New York Prieur C, Tarbouriech S, Gomes da Silva JM (2016) Wave equation with cone-bounded control laws. IEEE Trans Automat Control 61(11):3452–3463 Schwenninger FL (2020) Input-to-state stability for parabolic boundary contrl: Linear and semi-linear systems. In: Kerner J, Laasri H, Mugnolo D (eds) Control theory of infinite-dimensional systems. Birkhäuser, 83–116 Seidman TI, Li H (2001) A note on stabilization with saturating feedback. Discrete Contin Dyn Syst 7(2):319–328 Slemrod M (1989) Feedback stabilization of a linear control system in Hilbert space with an a priori bounded control. Math Control Signals Syst 2(3):265–285 Webb GF (1972) Continuous nonlinear perturbations of linear accretive operators in Banach spaces. J Funct Anal 10:191–203