Strong and weak-star stabilisation of bilinear systems on nonreflexive Banach spaces

References

• Ammari, K., & Nicaise, S. (2015). Stabilization of elastic systems by collocated feedback. Springer.
   Google Scholar
• Bacciotti, A. (1992). Local stabilizability of nonlinear control systems (Series on Advances in Mathematics for Applied Sciences, Volume 8). World Scientific.
   Google Scholar
• Balakrishnan, A. V. (2012). Applications of mathematics: Applied functional analysis. Springer Science and Business Media.
   Google Scholar
• Ball, J. M., & Slemrod, M. (1979). Feedback stabilization of distributed semilinear control systems. Applied Mathematics and Optimization, 5(1), 169–179. https://doi.org/10.1007/BF01442552
   Web of Science ®Google Scholar
• Banks, S. P. (1986). Stabilizability of finite and infinite-dimensional bilinear systems. IMA Journal of Mathematical Control and Information, 3(4), 255–271. https://doi.org/10.1093/imamci/3.4.255
   Web of Science ®Google Scholar
• Barbu, V. (2009). Nonlinear differential in Banach spaces. Springer.
   Google Scholar
• Beauchard, K., & Nersesyan, V. (2010). Semi-global weak stabilization of bilinear Schrödinger equations. Comptes Rendus de l Académie des Sciences Paris, Series I, 348(19–20), 1073–1078. https://doi.org/10.1016/j.crma.2010.09.002
   Google Scholar
• Benzaza, A., & Ouzahra, M. (2019). Weak and strong stabilisation of bilinear systems in a Banach space. International Journal of Control, 92(12), 2784–2790. https://doi.org/10.1080/00207179.2018.1459858
   Web of Science ®Google Scholar
• Berrahmoune, L. (1999). Stabilization and decay estimate for distributed bilinear systems. Systems Control Letters, 36, 3167–171. https://doi.org/10.1016/S0167-6911(98)00065-6
   Web of Science ®Google Scholar
• Berrahmoune, L. (2010). Stabilization of unbounded bilinear control systems in Hilbert space. Journal of Mathematical Analysis and Applications, 372(2), 645–655. https://doi.org/10.1016/j.jmaa.2010.06.010
   Web of Science ®Google Scholar
• Chen, M.-S. (1998). Exponential stabilization of a constrained bilinear system. Automatica, 34(8), 989–992. https://doi.org/10.1016/S0005-1098(98)00037-5
   Web of Science ®Google Scholar
• Fattorini, H. O. (1974). The time-optimal control problem in Banach spaces. Applied Mathematics and Optimization, 1(2), 163–188. https://doi.org/10.1007/BF01449028
   Web of Science ®Google Scholar
• Fattorini, H. O. (2001). A survey of the time optimal problem and the norm optimal problem in infinite dimension. CUBO, Mathematical Journal, 3, 147–169.
   Google Scholar
• Gunter, L., & Phillips, R. S. (1983). Dissipative operators in Banach space. Pacific Journal of Mathematics, 11(2), 979–998. https://doi.org/10.2140/pjm.1961.11.679
   Google Scholar
• Jurjevic, V., & Quinn, J. P. (1978). Controllability and stability. Journal of Differential Equations, 28(3), 381–389. https://doi.org/10.1016/0022-0396(78)90135-3
   Web of Science ®Google Scholar
• Kato, T. (1984). Nonlinear semigroups and evolution equations. Journal of the Mathematical Society of Japan, 19(4), 508–520. https://doi.org/10.2969/jmsj/01940508
   Google Scholar
• Khapalov, A. Y. (2010). Controllability of partial differential equations governed by multiplicative controls. Springer-Verlag.
   Google Scholar
• Khapalov, A. Y., & Mohler, R. R. (1998). Asymptotic stabilization of the bilinear time-invariant system via piecewise-constant feedback. Systems and Control Letters, 33(1), 47–54. https://doi.org/10.1016/S0167-6911(97)00094-7
   Web of Science ®Google Scholar
• Mohler, R. R. (1973). Bilinear control processes. Academic Press.
   Google Scholar
• Nagel, R., & Engel, K.-J. (2000). One parameter semi-groups for linear evolution equations. Springer-Verlag New York, Inc.
   Google Scholar
• Ouzahra, M. (2007a). Stabilization with decay estimate for a class of distributed bilinear systems. European Journal of Control, 13(5), 509–515. https://doi.org/10.3166/ejc.13.509-515
   Web of Science ®Google Scholar
• Ouzahra, M. (2007b). Exponential and weak stabilization of constrained bilinear systems. SIAM Journal on Control and Optimization, 48(6), 3962–3974. https://doi.org/10.1137/080739161
   Google Scholar
• Ouzahra, M. (2011). Exponential stabilization of distributed semilinear systems by optimal control. Journal of Mathematical Analysis and Applications, 380(1), 117–123. https://doi.org/10.1016/j.jmaa.2011.03.029
   Web of Science ®Google Scholar
• Ouzahra, M. (2012). Global stabilization of semilinear systems using switching controls. Automatica, 48(5), 837–843. https://doi.org/10.1016/j.automatica.2012.02.018
   Web of Science ®Google Scholar
• Ouzahra, M. (2017). Exponential stability of nondissipative linear system in Banach space and application to unbounded bilinear systems. Systems & Control Letters, 109(2), 53–62. https://doi.org/10.1016/j.sysconle.2017.08.010
   Google Scholar
• Ouzahra, M. (2020). Uniform exponential stabilization of nonlinear systems in Banach spaces. Mathematical Methods in the Applied Sciences, 43(12), 7311–7325. https://doi.org/10.1002/mma.v43.12
   Web of Science ®Google Scholar
• Pazy, A. (1983). Semi-groups of linear operators and applications to partial differential equations. Springer Verlag.
   Google Scholar
• Phelps, R. R. (1993). Convex functions, monotone operators and differentiability (2nd ed.). Springer-Verlag.
   Google Scholar
• Rhandi, A. (1998). Positivity and stability for a population equation with diffusion on. Positivity, 2(2), 101–113. https://doi.org/10.1023/A:1009721915101
   Web of Science ®Google Scholar
• Rhandi, A., & Schnaubelt, H. (1999). Asymptotic behaviour of a non-autonomous population equation with diffusion in L1. Discrete & Continuous Dynamical Systems. 5(3), 663–683. https://doi.org/10.3934/dcds.1999.5.663
   Web of Science ®Google Scholar
• Slemrod, M. (1978). Stabilization of bilinear control systems with applications to nonconservative problems in elasticity. SIAM Journal on Control and Optimization, 16(1), 131–141. https://doi.org/10.1137/0316010
   Web of Science ®Google Scholar