References
- Andrieu, V., & Praly, L. (2009). A unifying point of view on output feedback designs for global asymptotic stabilization. Automatica, 45, 1789–1798. https://doi.org/https://doi.org/10.1016/j.auto-matica.2009.04.015
- Angeli, D., Sontag, E. D., & Wang, Y. (2000). A characterization of integral input-to-state stability. IEEE Transactions on Automatic Control, 45, 1082–1097. https://doi.org/https://doi.org/10.1109/9.863594
- Bensoussan, A., Da Prato, G., Delfour, M. C., & Mitter, S. K. (1992). Representation and control of infinite dimensional systems. Birkhauser.
- Curtain, R. F., & Zwart, H. J. (1995). An introduction to infinite dimensional linear systems theory. Springer-Verlag.
- Damak, H., & Hammami, M. A. (2020). Asymptotic stability of a perturbed abstract differential equations in Banach spaces. Operators and Matrices, 14, 129–138. https://doi.org/https://doi.org/10.7153/oam-2020-14-10
- Dashkovskiy, S., & Mironchenko, A. (2013a). Input-to-state-stability of infinite-dimensional control systems. Mathematics of Control, Signals, and Systems, 25, 1–35. https://doi.org/https://doi.org/10.1007/s00498-012-0090-2
- Dashkovskiy, S., & Mironchenko, A. (2013b). Input-to-state stability of nonlinear impulsive systems. SIAM Journal on Control and Optimization, 51, 1962–1987. https://doi.org/https://doi.org/10.1137/120881993
- Dashkovskiy, S., Ruffer, B. S., & Wirth, F. R. (2007). An ISS small gain theorem for general networks. Mathematics of Control, Signals, and Systems, 19, 93–122. https://doi.org/https://doi.org/10.1007/s00498-007-0014-8
- Edwards, H., Lin, Y., & Wang, Y. (2000). On input-to-state stability for time varying nonlinear systems. In Proceedings of the 39th IEEE conference on decision and control (pp. 3501–3506). Sydney, Australia.
- Freeman, R. A, & Kokotovic, P. V (2008). Robust nonlinear control design: State-space and Lyapunov techniques. Birkhauser.
- Haimovich, H., & Mancilla-Aguilar, J. L. (2019). ISS implies iISS even for switched and time-varying systems (if you are careful enough). Automatica, 104, 154–164. https://doi.org/https://doi.org/10.1016/j.automatica.2019.02.057
- Jiang, Z. P, & Wang, Y. (2001). Input-to-state stability for discrete-time nonlinear systems. Automatica, 37, 857–869. https://doi.org/https://doi.org/10.1016/S0005-1098(01)00028-0
- Karafyllis, I., & Jiang, Z. P. (2011). Stability and stabilization of nonlinear systems. Springer.
- Karafyllis, I., & Krstic, M. (2017). ISS in different norms for 1-D parabolic PDEs with boundary disturbances. SIAM Journal on Control and Optimization, 55, 1716–1751. https://doi.org/https://doi.org/10.1137/16M1073753
- Kokotovic, P., & Arcak, M. (2001). Constructive nonlinear control: A historical perspective. Automatica, 37, 637–662. https://doi.org/https://doi.org/10.1016/S0005-1098(01)00002-4
- Mazenc, F., Malisoff, M., & Niculescu, S. I. (2015). Stability analysis for systems with time-varying delay: Trajectory based approach. In 54th IEEE conference on decision and control (pp. 1811–1816). Ozaka, Japan.
- Mazenc, F., & Prieur, C. (2011). Strict Lyapunov functions for semilinear parabolic partial differential equations. Mathematical Control & Related Fields, 1, 231–250. https://doi.org/https://doi.org/10.3934/mcrf.2011.1.231
- Mironchenko, A. (2016). Local input-to-state stability: Characterizations and counterexamples. Systems & Control Letters, 87, 23–28. https://doi.org/https://doi.org/10.1016/j.sysconle.2015.10.014
- Mironchenko, A., & Ito, H. (2015). Construction of Lyapunov functions for interconnected parabolic systems: An iISS approach. SIAM Journal on Control and Optimization, 53, 3364–3382. https://doi.org/https://doi.org/10.1137/14097269X
- Mironchenko, A., & Ito, H. (2016). Characterizations of integral input-to-state-stability for binlinear systems in infinite dimensions. Mathematical Control & Related Fields, 6, 447–466. https://doi.org/https://doi.org/10.3934/mcrf
- Mironchenko, A., Karafyllis, I., & Krstic, M. (2019). Monotonicity methods for input-to-state stability of nonlinear parabolic PDEs with boundary disturbances. SIAM Journal on Control and Optimization, 57(1), 510–532. https://doi.org/https://doi.org/10.1137/17M1161877
- Mironchenko, A., & Prieur, C. (2020). Input-to-state stability of infinite-dimensional systems: Recent results and open questions. SIAM Review, 62(3), 529–614. https://doi.org/https://doi.org/10.1137/19M1291248
- Mironchenko, A., & Wirth, F. (2018a). Characterizations of input-to-state stability for infinite-dimensional systems. IEEE Transactions on Automatic Control, 63, 1602–1617. https://doi.org/https://doi.org/10.1109/TAC.2017.2756341
- Mironchenko, A., & Wirth, F. (2018b). Lyapunov characterization of input-to-state-stability for semilinear control systems over Banach spaces. Systems & Control Letters, 119, 64–70. https://doi.org/https://doi.org/10.1016/j.sysconle.2018.07.007
- Mironchenko, A., & Wirth, F. (2019). Non-coercive Lyapunov functions for infinite-dimensional systems. Journal of Differential Equations, 105, 7038–7072. https://doi.org/https://doi.org/10.1016/j.jde.2018.11.026
- Mitrinovic, D. S., Pecaric, J. E., & Fink, M. (1991). Inequalities involving functions and their integrals and derivatives. Kluwer Academic Publishers Group.
- Noroozi, N., Khayatian, A., Ahmadizadeh, S., & Karimi, H. R. (2014). On integral input-to-state stability for a feedback interconnection of parameterised discrete-time systems. International Journal of Systems Science, 47, 1598–1614. https://doi.org/https://doi.org/10.1080/00207721.2014.942242
- Pazy, A. (1983). Semigroup of linear operators and applications to partial differential equations. Springer.
- Prieur, C., & Mazenc, F. (2012). ISS-Lyapunov functions for time-varying hyperbolic systems of balance laws. Mathematics of Control, Signals, and Systems, 24, 111–134. https://doi.org/https://doi.org/10.1007/s00498-012-0074-2
- Respondek, J. S. (2007). Numerical analysis of controllability of diffusive-convective system with limited manipulating variables. International Communications in Heat and Mass Transfer, 34, 934–944. https://doi.org/https://doi.org/10.1016/j.icheatmass-transfer.2007.04.005
- Respondek, J. S. (2010). Numerical simulation in the partial differential equation controllability analysis with physically meaningful constraints. Mathematics and Computers in Simulation, 81, 120–132. https://doi.org/https://doi.org/10.1016/j.matcom.2010.07.016
- Royden, H., & Fitzpatrick, P. (2010). Real analysis. Prentice-Hall.
- Sontag, E. D. (1989). Smooth stabilization implies coprime factorization. IEEE Transactions on Automatic Control, 34, 435–443. https://doi.org/https://doi.org/10.1109/9.28018
- Sontag, E. D. (1998). Comments on integral variants of ISS. Systems & Control Letter, 34, 93–100. https://doi.org/https://doi.org/10.1016/S0167-6911(98)00003-6
- Sontag, E. D., & Teel, A. (1995). Changing supply functions in input/state stable systems. IEEE Transactions on Automatic Control, 40, 1476–1478. https://doi.org/https://doi.org/10.1109/9.402246
- Teschl, G. (2012). Ordinary differential equations and dynamical systems. Graduate studies in mathematics. American Mathematical Society.