A new method to study ILC problem for time-delay linear systems

Balachandran, B, Kalmár-Nagy, T, Gilsinn, DE: Delay Differential Equations. Springer, Berlin (2009)

He, J: Variational iteration method for delay differential equations. Commun. Nonlinear Sci. Numer. Simul. 2, 235-236 (1997)

Wang, Q, Liu, XZ: Exponential stability for impulsive delay differential equations by Razumikhin method. J. Math. Anal. Appl. 309, 462-473 (2005)

Wen, Y, Zhou, XF, Zhang, Z, Liu, S: Lyapunov method for nonlinear fractional differential systems with delay. Nonlinear Dyn. 82, 1015-1025 (2015)

Abbas, S, Benchohra, M, Rivero, M, Trujillo, JJ: Existence and stability results for nonlinear fractional order Riemann-Liouville Volterra-Stieltjes quadratic integral equations. Appl. Math. Comput. 247, 319-328 (2014)

Zhang, GL, Song, MH, Liu, MZ: Exponential stability of the exact solutions and the numerical solutions for a class of linear impulsive delay differential equations. J. Comput. Appl. Math. 285, 32-44 (2015)

Uchiyama, M: Formulation of high-speed motion pattern of a mechanical arm by trial. Trans. Soc. Instrum. Control Eng. 14, 706-712 (1978)

Arimoto, S, Kawamura, S: Bettering operation of robots by learning. J. Robot. Syst. 1, 123-140 (1984)

Xu, JX, Xu, J: On iterative learning for different tracking tasks in the presence of time-varying uncertainties. IEEE Trans. Syst. Man Cybern. B 34, 589-597 (2004)

Ahn, HS, Moore, KL, Chen, YQ: Iterative Learning Control: Robustness and Monotonic Convergence in the Iteration Domain. Communications and Control Engineering Series. Springer, Berlin (2007)

Luo, Y, Chen, YQ: Fractional order controller for a class of fractional order systems. Automatica 45, 2446-2450 (2009)

Li, Y, Chen, YQ, Ahn, HS: On the P D α $PD^{\alpha}$ -type iterative learning control for the fractional-order nonlinear systems. In: Proc. Amer. Control Conference, pp. 4320-4325 (2011)

Bien, ZZ, Xu, JX (eds.): Iterative Learning Control: Analysis, Design, Integration and Applications. Springer, Media (2012)

Li, ZG, Chang, YW, Soh, YC: Analysis and design of impulsive control systems. IEEE Trans. Autom. Control 46, 894-897 (2001)

Sun, MX: Robust convergence analysis of iterative learning control systems. Control Theory Appl. 15, 320-326 (1998)

Lee, HS, Bien, Z: Design issues on robustness and convergence of iterative learning controller. Intell. Autom. Soft Comput. 8, 95-106 (2002)

Sun, MX, Chen, YQ, Huang, BJ: High order iterative learning control system for nonlinear time-delay systems. Acta Autom. Sin. 20, 360-365 (1994)

Sun, MX: Iterative learning control algorithms for uncertain time-delay systems (I). J. Xi’an Instit. Technol. 17, 259-266 (1997)

Sun, MX: Iterative learning control algorithms for uncertain time-delay systems (II). J. Xi’an Instit. Technol. 18, 1-8 (1998)

Khusainov, DY, Shuklin, GV: Linear autonomous time-delay system with permutation matrices solving. Stud. Univ. Žilina Math. Ser. 17, 101-108 (2003)

Khusainov, DY, Shuklin, GV: Relative controllability in systems with pure delay. Int. J. Appl. Math. 2, 210-221 (2005)

Medved’, M, Pospišil, M, Škripokvá, L: Stability and the nonexistence of blowing-up solutions of nonlinear delay systems with linear parts defined by permutable matrices. Nonlinear Anal. TMA 74, 3903-3911 (2011)

Medveď, M, Pospišil, M: Sufficient conditions for the asymptotic stability of nonlinear multidelay differential equations with linear parts defined by pairwise permutable matrices. Nonlinear Anal. TMA 75, 3348-3363 (2012)

Diblik, J, Fečkan, M, Pospišil, M: Representation of a solution of the Cauchy problem for an oscillating system with two delays and permutable matrices. Ukr. Math. J. 65, 58-69 (2013)

Boichuk, A, Diblik, J, Khusainov, D, Růžičková, M: Fredholm’s boundary-value problems for differential systems with a single delay. Nonlinear Anal. TMA 72, 2251-2258 (2010)

Boichuk, A, Diblik, J, Khusainov, D, Růžičková, M: Boundary value problems for delay differential systems. Adv. Differ. Equ. 2010, Article ID 593834 (2010)

Boichuk, A, Diblik, J, Khusainov, D, Růžičková, M: Boundary-value problems for weakly nonlinear delay differential systems. Abstr. Appl. Anal. 2011, Article ID 631412 (2011)

Ortega, JM, Rheinboldt, WC: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, San Diego (1970)