EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 27 (2021) ESAIM: COCV, 27 (2021) 53 References
Open Access
Issue
ESAIM: COCV
Volume 27, 2021
Article Number 53
Number of page(s) 37
DOI https://doi.org/10.1051/cocv/2021051
Published online 04 June 2021
  1. B. Augner, Well-posedness and stability of linear port-Hamiltonian systems with nonlinear boundary feedback. SIAM J. Control Optim. 57 (2019) 1818–1844. [CrossRef] [Google Scholar]
  2. B. Augner, Stabilisation of infinite-dimensional port-Hamiltonian systems via dissipative boundary feedback. PhD. thesis, Universität Wuppertal (2016). [Google Scholar]
  3. G. Bastin and J.-M. Coron, Stability and boundary stabilization of 1-D hyperbolic systems. Birkhäuser (2016). [CrossRef] [Google Scholar]
  4. F.H. Clarke, Y.S. Ledyaev and R.J. Stern, Asymptotic stability and smooth Lyapunov functions. J. Differ. Equ. 149 (1998) 69–114. [CrossRef] [MathSciNet] [Google Scholar]
  5. R. Curtain and H. Zwart, Introduction to infinite-dimensional systems theory. A state-space approach. Springer (2020). [CrossRef] [Google Scholar]
  6. S. Dashkovskiy and A. Mironchenko, Input-to-state stability of infinite-dimensional control systems. Math. Contr. Sign. Syst. 25 (2013) 1–35. [CrossRef] [Google Scholar]
  7. S. Dashkovskiy, A. Mironchenko, J. Schmid and F. Wirth, Stability of infinitely many interconnected systems. Conference proceedings of the 11th IFAC Symposium on Nonlinear Control Systems, IFAC-PapersOnLine 52 (2019) 937–942. [Google Scholar]
  8. S. Dashkovskiy, O. Kapustyan and J. Schmid, A local input-to-state stability result w.r.t. attractors of nonlinear reaction–diffusion equations. Math. Contr. Sign. Syst. 32 (2020) 309–326. [CrossRef] [Google Scholar]
  9. V. Duindam, A. Macchelli, S. Stramigioli and H. Bruyninckx (editors) Modeling and control of complex physical systems – the port-Hamiltonian approach. Springer (2009). [CrossRef] [Google Scholar]
  10. M.S. Edalatzadeh and K. Morris, Stability and well-posedness of a nonlinear railway track model. IEEE Control Syst. Lett. 3 (2019). [Google Scholar]
  11. H.O. Fattorini, Boundary control systems. SIAM J. Contr. 6 (1968) 349–388. [Google Scholar]
  12. B. Jacob and H. Zwart, Linear port-Hamiltonian systems on infinite-dimensional spaces. Birkäuser (2012). [Google Scholar]
  13. B. Jacob, K. Morris and H. Zwart, C0-semigroups for hyperbolic partial differential equations on a one-dimensional spatial domain. J. Evol. Equ. 15 (2015) 493–502. [CrossRef] [Google Scholar]
  14. B. Jacob and J. Kaiser, Well-posedness of networks for 1-D hyperbolic partial differential equations. J. Evol. Equ. 19 (2019) 91–109. [CrossRef] [Google Scholar]
  15. B. Jacob, R. Nabiullin, J. Partington and F. Schwenninger, Infinite-dimensional input-to-state stability and Orlicz spaces. SIAM J. Contr. Optim. 56 (2018) 868–889. [CrossRef] [Google Scholar]
  16. B. Jacob and F. Schwenninger, Input-to-state stability of unbounded bilinear control systems. arXiv:1811.08470 (2018). [Google Scholar]
  17. B. Jacob, F.L. Schwenninger and H. Zwart, On continuity of solutions for parabolic control systems and input-to-state stability. J. Differ. Equ. 266 (2018) 6284–6306. [CrossRef] [Google Scholar]
  18. B. Jacob, A. Mironchenko, J.R. Partington and F. Wirth, Non-coercive Lyapunov functions for input-to-state stability of infinite-dimensional systems. SIAM J. Contr. Optim. 58 (2020) 2952–2978. [CrossRef] [Google Scholar]
  19. B. Jacob, F. Schwenninger and L. Vorberg, Remarks on input-to-state stability of collocated systems with saturated feedback. arXiv:2001.01636 (2020). [Google Scholar]
  20. B. Jayawardhana and G. Weiss, State convergence of poassive nonlinear systems with L2 input. IEEE Trans. Autom. Contr. 54 (2009) 1723–1727. [CrossRef] [Google Scholar]
  21. H.G. Kankanamalage, Y. Lin and Y. Wang, On Lyapunov-Krasovskii characterizations of input-to-output stability. IFAC-PapersOnLine 50 (2017) 14362–14367. [CrossRef] [Google Scholar]
  22. I. Karafyllis and M. Krstic, ISS with respect to boundary disturbances for 1-D parabolic PDEs. IEEE Trans. Automat. Contr. 61 (2016) 3712–3724. [CrossRef] [Google Scholar]
  23. I. Karafyllis and M. Krstic, ISS in different norms for 1-D parabolic PDEs with boundary disturbances. SIAM J. Contr. Optim. 55 (2017) 1716–1751. [CrossRef] [Google Scholar]
  24. I. Karafyllis and M. Krstic, Input-to-State Stability for PDEs. Springer (2019). [Google Scholar]
  25. C. Kawan, A. Mironchenko, A. Swikir, N. Noroozi and M. Zamani, A Lyapunov-based ISS small-gain theorem for infinite networks. IEEE Trans. Autom. Contr. (2019) doi: 10.1109/TAC.2020.3042410. [Google Scholar]
  26. Y. Le Gorrec, H. Zwart and B. Maschke, Dirac structures and boundary control systems associated with skew-symmetric differential operators. SIAM J. Contr. Optim. 44 (2005) 1864–1892. [CrossRef] [MathSciNet] [Google Scholar]
  27. F. Mazenc and C. Prieur, Strict Lyapunov functions for semilinear parabolic partial differential equations. Math. Contr. Rel. Fields 1 (2011) 231–250. [CrossRef] [Google Scholar]
  28. M. Miletic, D. Stürzer, A. Arnold and A. Kugi, Stability of an Euler-Bernoulli beam with a nonlinear dynamic feedback system. IEEE Trans. Autom. Contr. 61 (2016) 2782–2795. [CrossRef] [Google Scholar]
  29. A. Mironchenko, Local input-to-state stability: characterizations and counterexamples. Syst. Contr. Lett. 87 (2016) 23–28. [CrossRef] [Google Scholar]
  30. A. Mironchenko and F. Wirth, Characterizations of input-to-state stability for infinite-dimensional systems. IEEE Trans. Autom. Contr. 63 (2018) 1692–1707. [CrossRef] [Google Scholar]
  31. A. Mironchenko and F. Wirth, Lyapunov characterization of input-to-state stability for semilinear control systems over Banach spaces. Syst. Contr. Lett. 119 (2018) 64–70. [CrossRef] [Google Scholar]
  32. A. Mironchenko, I. Karafyllis and M. Krstic, Monotonicity methods for input-to-state stability of nonlinear parabolic PDEs with boundary disturbances. SIAM J. Contr. Optim. 57 (2019) 510–532. [CrossRef] [Google Scholar]
  33. A. Mironchenko, Criteria for input-to-state practical stability. IEEE Trans. Autom. Contr. 64 (2019) 298–304. [CrossRef] [Google Scholar]
  34. A. Mironchenko, Small gain theorems for general networks of heterogeneous infinite-dimensional systems. arXiv:1901.03747 (2019). [Google Scholar]
  35. A. Mironchenko, C. Kawan and J. Glück, Nonlinear small-gain theorems for input-to-state stability of infinite interconnections. arXiv:2007.05705 (2020). [Google Scholar]
  36. A. Mironchenko and C. Prieur, Input-to-state stability of infinite-dimensional systems: recent results and open questions. SIAM Rev. 62 (2020) 529–614. [CrossRef] [Google Scholar]
  37. R. Nabiullin and F. Schwenninger, Strong input-to-state stability for infinite dimensional linear systems. Math. Contr. Sign. Syst. 30 (2018). [Google Scholar]
  38. J. Oostveen, Strongly stabilizable distributed parameter systems. SIAM Frontiers Appl. Math. (2000). [Google Scholar]
  39. A. Pazy, Semigroups of linear operators and applications to partial differential equations. Springer (1983). [CrossRef] [Google Scholar]
  40. P. Pepe, On Liapunov–Krasovskii functionals under Caratheodory conditions. Automatica 43 (2007) 701–706. [CrossRef] [Google Scholar]
  41. H. Ramirez, Y. Le Gorrec, A. Macchelli and H. Zwart, Exponential stabilization of boundary controlled port-Hamiltonian systems with dynamic feedback. IEEE Trans. Autom. Contr. 59 (2014) 2849–2855. [CrossRef] [Google Scholar]
  42. H. Ramirez, H. Zwart and Y. Le Gorrec, Stabilization of infinite-dimensional port-Hamiltonian systems by nonlinear dynamic boundary control. Automatica 85 (2017) 61–69. [CrossRef] [Google Scholar]
  43. J. Schmid and H. Zwart, Stabilization of port-Hamiltonian systems by nonlinear boundary control in the presence of disturbances. Conference proceedings of the 23rd Symposium on Mathematical Theory of Networks and Systems (2018) 570–575. [Google Scholar]
  44. J. Schmid, Stabilization of port-Hamiltonian systems with discontinuous energy densities. arXiv:1809.00857 (2018). Accepted provisionally in Evol. Equ. Contr. Th.. [Google Scholar]
  45. J. Schmid, Weak input-to-state stability: characterizations and counterexamples. Math. Contr. Sign. Syst. 31 (2019) 433–454. [CrossRef] [Google Scholar]
  46. J. Schmid, S. Dashkovskiy, B. Jacob and H. Laasri, Well-posedness of non-autonomous semilinear systems. Conference proceedings of the 11th Symposium on Nonlinear Control Systems, IFAC-PapersOnLine 52 (2019) 216–220. [Google Scholar]
  47. J. Schmid, Well-posedness and stability of non-autonomous semilinear input-output systems. arXiv:1904.10376 (2019). Accepted provisionally in Evol. Equ. Contr. Th.. [Google Scholar]
  48. J. Schmid, Infinite-time admissibility under compact perturbations. In: J.Kerner, H. Laasri, D. Mugnolo (eds.), Control theory of infinite-dimensional systems, Operator Theory: Advances and Applications 277 (2020) 73–82. [CrossRef] [Google Scholar]
  49. J. Schmid, O. Kapustyan and S. Dashkovskiy, Asymptotic gain results for attractors of semilinear systems. arXiv:1909.06302 (2019). Accepted for publication in Math. Contr. Rel. Fields. [Google Scholar]
  50. F. Schwenninger, Input-to-state stability for parabolic boundary control: linear and semi-linear systems. In: J. Kerner, H. Laasri, D. Mugnolo (eds.), Control theory of infinite-dimensional systems, Operator Theory: Advances and Applications 277 (2020) 83–116. [CrossRef] [Google Scholar]
  51. A. Tanwani, C. Prieur and S. Tarbouriech, Disturbance-to-state stabilization and quantized control for linear hyperbolic systems. arXiv:1703.00302 (2017). [Google Scholar]
  52. M. Tucsnak and G. Weiss, Well-posed systems – the LTI case and beyond. Automatica 50 (2014) 1757–1779. [CrossRef] [MathSciNet] [Google Scholar]
  53. J. Villegas, A port-Hamiltonian approach to distributed-parameter systems. Ph.D. thesis, Universiteit Twente (2007). [Google Scholar]
  54. J. Villegas, H. Zwart, Y. Le Gorrec and B. Maschke, Exponential stability of a class of boundary control systems. IEEE Trans. Autom. Contr. 54 (2009) 142–147. [CrossRef] [Google Scholar]
  55. G. Weiss, Admissibility of unbounded control operators. SIAM J. Contr. Optim. 27 (1989) 527–545. [Google Scholar]
  56. J. Zheng and G. Zhu, Input-to-state stability with respect to boundary disturbances for a class of semi-linear parabolic equations. Automatica 97 (2018) 271–277. [Google Scholar]
  57. J. Zheng and G. Zhu, A De Giorgi iteration-based approach for the establishment of ISS properties for burgers–equation with boundary and in-domain disturbances . IEEE Trans. Automat. Contr. 64 (2019) 3476–3483. [Google Scholar]
  58. J. Zheng and G. Zhu, A weak maximum principle-based approach for input-to-state stability of nonlinear parabolic PDEs with boundary disturbances. Math. Control Signals Syst. 32 (2020) 157–176. [Google Scholar]
  59. H. Zwart, H. Ramirez and Y. Le Gorrec, Asymptotic stability for a class of boundary control systems with non-linear damping. In: The second IFAC workshop on control of systems governed by partial differential equations (CPDE). Bertinoro, Italy (2016). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.