Stability and feedback stabilizability of delay periodic differential equations with pairwise permutable matrix functions

References

[1] Arnold, V. I.: On matrices depending on parameters, Russian Math. Surveys 26 (1971), 29–43.10.1007/978-3-642-31031-7_28Search in Google Scholar

[2] Belikov, J.—Bartosiewicz, Z.: Stability and stabilizability of linear time-delay systems on homogeneous time scales, Proc. Est. Acad. Sci. 66 (2017), 124–136.10.3176/proc.2017.2.02Search in Google Scholar

[3] Bihari, I. A.: A generalization of a lemma of Bellman and its application to uniqueness problem of differential equation, Acta Math. Hungar. 7 (1956), 81–94.10.1007/BF02022967Search in Google Scholar

[4] Brunovský, P.: Controllability and linear closed-loop controls in linear periodic systems, J. Differential Equations 6 (1969), 296–313.10.1016/0022-0396(69)90019-9Search in Google Scholar

[5] Hartman, P.: Ordinary Differential Equations, John Wiley & Sons, Inc., New York, 1964.Search in Google Scholar

[6] Hale, J. K.—Verduyn Lunel, S. M.: Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993.10.1007/978-1-4612-4342-7Search in Google Scholar

[7] Higham, N. J.: Functions of Matrices, Theory and Computation, SIAM, Philadelphia, 2008.10.1137/1.9780898717778Search in Google Scholar

[8] Khusainov, D. Ya.—Shuklin, G. V.: Linear autonomous time-delay system with permutation matrices solving, Stud. Univ. Žilina, Math. Ser. 17 (2003), 101–108.Search in Google Scholar

[9] Medveď, M.—Pospíšil, M.: Sufficient conditions for the asymptotic stability of nonlinear multidelay differential equations with linear parts defined by pairwise permutable matrices, Nonlinear Anal. Theory Methods Appl. 75 (2012), 3348–3363.10.1016/j.na.2011.12.031Search in Google Scholar

[10] Medveď, M.—Pospíšil, M.: Representation of solutions of systems of linear differential equations with multiple delays and linear parts given by non-permutable matrices, Nonlinear Oscil. 19 (2016), 521–532.Search in Google Scholar

[11] Pereira, E.—Rosa, C.: A method to construct sets of commuting matrices, J. Math. Res. 5 (2013), 1–7.10.5539/jmr.v5n3p1Search in Google Scholar

[12] Pinto, M.: Integral inequalities of Bihari-type and applications, Funkcial. Ekvac. 33 (1990), 387–403.Search in Google Scholar

[13] Popov, V. M.: Hyperstability and optimality of automatic systems with several control functions, Rev. Roumaine Sci. Techn., Electrotechn. et Energ. 9 (1964), 629–690.Search in Google Scholar

[14] Popov, V. M.: Hyperstabilitatea Sistemelor Automate, Editura Academiei Rep. Soc. Romania, Bucharest, 1966.Search in Google Scholar

[15] Pospíšil, M.: Representation and stability of solutions of systems of functional differential equations with multiple delays, Electron. J. Qual. Theory Differ. Equ. 54 (2012), 1–30.10.14232/ejqtde.2012.1.54Search in Google Scholar

[16] Pospíšil, M.: Relative controllability of neutral differential equations with a delay, SIAM J. Control Optim. 55 (2017), 835–855.10.1137/15M1024287Search in Google Scholar

[17] Pospíšil, M.—Jaroš, F.: On the representation of solutions of delayed differential equations via Laplace transform, Electron. J. Qual. Theory Differ. Equ. 117 (2016), 1–13.10.14232/ejqtde.2016.1.117Search in Google Scholar

[18] Seuret, A.—Johansson, H.: Stabilization of time-delay systems through linear differential equations using a descriptor representation, Proceedings of the European Control Conference, 2009, 4727–4732.10.23919/ECC.2009.7075147Search in Google Scholar

[19] Sieber, J.: Generic stabilizability for time-delayed feedback control, Proc. Roy. Soc. Edinburgh Sect. A 472 (2016), Art. ID 20150593, 19 pp.10.1098/rspa.2015.0593Search in Google Scholar PubMed PubMed Central

[20] Wang, G.—Xu, Y.: Periodic stabilization for linear time-periodic ordinary differential equations, ESAIM: COCV 20 (2014), 269–314.10.1051/cocv/2013064Search in Google Scholar

[21] Zabczyk, J.: Mathematical Control Theory: An Introduction. Systems and Control: Foundations and Applications, Birkhauser Boston, Inc., Boston, MA, 1992.Search in Google Scholar