Boundary-value problems for the Lyapunov equation. II
DOI:
https://doi.org/10.3842/umzh.v76i5.7786Keywords:
псевдообернені за Муром-Пенроузом оператори, input-to-state stabilityAbstract
UDC517.923
We investigate the bifurcation conditions of the solutions for the nonlinearly perturbed Lyapunov equation. Statements of boundary-value problems are proposed for the coupled systems of Lyapunov equations.
References
О. Бойчук, Є. Панасенко, О. Покутний, Крайові задачі для рівняння Ляпунова, I, Укр. мат. журн., 76, № 3, 353–372 (2024).
А. А. Бойчук, В. Ф. Журавлев, А. М. Самойленко, Обобщенно-обратные операторы и нетеровы краевые задачи, Институт математики НАН Украины, Киев (1995).
S. Dashkovskiy, A. Mironchenko, Input-to-state stability of infinite-dimensional control systems; arXiv.org (1202.3325 [math.OC]): 1–33 (2012); DOI: https://DOI.org/10.48550/arXiv.1202.3325.
S. Dashkovskiy, A. Mironchenko, Input-to-state stability of nonlinear impulsive systems; arXiv.org (1212.5481 [math.DS]), 1–26 (2012); DOI: https://doi.org/10.48550/arXiv.1212.5481.
S. Dashkovskiy, O. Kapustyan, V. Slynko, Well-posedness and robust stability of a nonlinear ODE-PDE system; arXiv.org (2103.15747 [math.AP]), 1–45 (2021); DOI: https://doi.org/10.48550/arXiv.2103.15747.
B. Jacob, A. Mironchenko, Noncoercive Lyapunov functions for input-to-state stability of infinite-dimensional systems; arXiv.org (1911.01327 [math.OC]), 1–27 (2019); DOI: https://doi.org/10.48550/arXiv.1911.01327.
A. M. Kovalev, A. A. Martynyuk, O. A. Boichuk, A. G. Mazko, R. I. Petryshyn, V. Yu. Slyusarchuk, A. L. Zuyev, V. I. Slyn’ko, Novel qualitative methods of nonlinear mechanics and their application to the analysis of multifrequency oscillations, stability, and control problems, Nonlinear Dyn. and Syst. Theory, 9, № 2, 117–145 (2009).
A. Mironchenko, H. Ito, Construction of Lyapunov functions for interconnected parabolic systems: an iISS approach; arXiv.org (1410.3058 [math.DS]), 1–20 (2014); DOI: https://doi.org/10.48550/arXiv.1410.3058.
A. Mironchenko, H. Ito, Integral input-to-state stability of bilinear infinite-dimensional systems, Proc. of the 53th IEEE Conference on Decision and Control, Los Angeles, California, (2014), p. 3115–3160.
A. Mironchenko, C. Prieur, Input-to-state stability of infinite-dimensional systems: recent results and open questions; arXiv.org (1910.01714 [math.OC]), 1–83 (2020); DOI: https://doi.org/10.48550/arXiv.1910.01714.
A. Mironchenko, V. Slynko, Dwell-time stability conditions for infinite dimensional impulsive systems; arXiv.org (2106.11224 [math.DS]), 1–15 (2021); DOI: https://doi.org/10.48550/arXiv.2106.11224.
A. Mironchenko, F. Wirth, Lyapunov characterization of input-to-state stability for semilinear control systems over Banach spaces, Systems and Control Lett., 119, 64–70 (2018). DOI: https://doi.org/10.1016/j.sysconle.2018.07.007
A. Mironchenko, F. Wirth, Characterizations of input-to-state stability for infinite-dimensional systems; arXiv.org (1701.08952 [math.OC]), 1–16 (2017); DOI: https://doi.org/10.48550/arXiv.1701.08952.
E. D. Sontag, Comments on integral variants of ISS, Systems and Control Lett., 34, № 1-2, 93–100 (1998). DOI: https://doi.org/10.1016/S0167-6911(98)00003-6
E. D. Sontag, Smooth stabilization implies coprime factorization, IEEE Trans. Automat. Control, 34, № 4, 435–443 (1989).
E. D. Sontag, Y. Wang, On characterizations of the input-to-state stability property, Systems and Control Lett., 24, № 5, 351–359 (1995).
