[1] Agarwal R.P., 2000. Difference Equations and Inequalities: Theory, Methods, and Applications. New
York: Marcel Dekker, Inc.
[2] Bayat, F., Mobayen, S. and Hatami, T., 2018. Composite nonlinear feedback design for discretetime
switching systems with disturbances and input saturation. Int. J. Syst. Sci., 49(11), pp. 2362–2372.
doi: https://doi.org/10.1080/00207721.2018.1501830
[3] Elloumi, S., Mechichi, A.K. and Braiek, N.B., 2013. On quadratic optimal control of nonlinear
discretetime systems. 10th International MultiConferences on Systems, Signals & Devices , Ham
mamet, Tunisia. doi: http://dx.doi.org/10.1109/SSD.2013.6564124
[4] Hassan Abadi, M., Mahmoudzadeh Vaziri, A. and Jajarmi, A., 2019. On a new and efficient numerical
technique to solve a class of discretetime nonlinear optimal control problems. J. Eur. des Syst. Autom.,
52(3), pp. 305–316. doi: https://doi.org/10.18280/jesa.520312
[5] Jajarmi, A. and Baleanu, D., 2018. Optimal control of nonlinear dynamical systems based on a new
parallel eigenvalue decomposition approach. Optim. Control Appl. Methods, 39(2), pp. 1071–1083.
doi: https://doi.org/10.1002/oca.2397
[6] Jajarmi, A. and Hajipour, M., 2017. An efficient parallel processing optimal control
scheme for a class of nonlinear composite systems. Acta. Math. Sci., 37(3), pp. 703–721.
doi: https://doi.org/10.1016/S02529602(17)300322
[7] Jajarmi, A., Pariz, N., Effati, S. and Vahidian Kamyad, A., 2012. Infinite horizon optimal control for
nonlinear interconnected largescale dynamical systems with an application to optimal attitude control.
Asian J. Control, 14(5), pp. 1239–1250. doi: https://doi.org/10.1002/asjc.452
[8] Janssen, L.A.L., Besselink, B., Fey, R.H.B. and van de Wouw, N., 2024. Modular model reduction
of interconnected systems: A robust performance analysis perspective. Automatica, 160, p. 111423.
doi: https://doi.org/10.1016/j.automatica.2023.111423
[9] Jordan, B.W. and Polak, E., 1964. Theory of a class of discrete optimal control systems, J. Electron.
Control, 17(6), pp. 697–711. doi: https://doi.org/10.1080/00207216408937740
[10] Khatibi, M. and Shanechi, H.M., 2011. Using modal series to analyze the transient response of oscil
lators. Int. J. Circ. Theor. App., 39(2), pp. 127–134. doi: https://doi.org/10.1002/cta.621
[11] Khatibi, M. and Shanechi, H.M., 2015. Using a modified modal Series to analyse weakly nonlinear circuits. Int. J. Electron., 102(9), pp. 1457–1474. doi: https://doi.org/10.1080/00207217.2014.982212
[12] Mehraeen, S. and Jagannathan, S., 2011. Decentralized optimal control of a class of interconnected nonlinear discretetime systems by using online HamiltonJacobiBellman formulation. IEEE Trans.
Neural Netw., 22(11), pp. 1757–1769. doi: https://doi.org/10.1109/TNN.2011.2160968
[13] Molloy, T.L., Ford, J.J. and Perez, T., 2018. Finitehorizon inverse opti
mal control for discretetime nonlinear systems. Automatica, 87, pp. 442–446.
doi: https://doi.org/10.1016/j.automatica.2017.09.023
[14] Pariz, N., 2001. Analysis of Nonlinear System Behavior: The Case of Stressed Power Systems. Iran: PhD Thesis.
[15] Pariz, N., Shanechi, H.M. and Vaahedi, E., 2003. Explaining and validating stressed
power systems behavior using modal series. IEEE Trans. Power. Syst., 18(2), pp. 778–785.
doi: https://doi.org/10.1109/TPWRS.2003.811307
[16] Sajjadi, S.S., Pariz, N., Karimpour, A. and Jajarmi, A., 2014. An offline NMPC strategy for
continuoustime nonlinear systems using an extended modal series method. Nonlinear Dyn., 78(4),
pp. 2651–2674. doi: https://doi.org/10.1007/s1107101416166
[17] Shankar, S., 1999. Nonlinear Systems: Analysis, Stability, and Control. New York: SpringerVerlag.
[18] Soltani, S., Pariz, N. and Ghazi R., 2009. Extending the perturbation technique to the
modal representation of nonlinear systems. Electr. Pow. Syst. Res., 79(8), pp. 1209–1215.
doi: https://doi.org/10.1016/j.epsr.2009.02.011
[19] Song, R., Xiao, W. and Sun, C., 2014. A new selflearning optimal control laws for a class
of discretetime nonlinear systems based on ESN architecture. Sci. China Inf. Sci., 57, pp. 1–10.
doi: http://dx.doi.org/10.1007/s114320134954y
[20] Song, Y., Liu, Y. and Zhao, W., 2024. Approximately bisimilar symbolic model for
discretetime interconnected switched system. IEEE/CAA J. Autom. Sin., 11(0), pp. 1–3.
doi: https://doi.org/10.1109/JAS.2023.123927
[21] Tang, G.Y. and Wang, H.H., 2005. Successive approximation approach of opti
mal control for nonlinear discretetime systems. Int. J. Syst. Sci., 36(3), pp. 153–161.
doi: https://doi.org/10.1080/00207720512331338076
[22] Tang, G.Y., Xie, N. and Liu, P., 2005. Sensitivity approach to optimal control for affine nonlin
ear discretetime systems. Asian J. Control, 7(4), pp. 448–454. doi: https://doi.org/10.1111/j.1934
6093.2005.tb00408.x
[23] Wei, Q. and Li, T., 2024. Constrainedcost adaptive dynamic programming for optimal control
of discretetime nonlinear systems. IEEE Trans. Neural Netw. Learn. Syst., 35(3), pp. 3251–3264.
doi: https://doi.org/10.1109/TNNLS.2023.3237586
[24] Wen, P., Wang, M. and Dai, S.L., 2024. Cooperative learning eventtriggered control for discretetime
nonlinear multiagent systems by internal and external interaction topology. Int. J. Robust Nonlinear
Control, 34(3), pp. 1541–1565. doi:
https://doi.org/10.1002/rnc.7044
[25] Yu, T. and Xiong, J., 2023. Decentralised H∞ filtering of interconnected discretetime systems. Int.
J. Control, 96(6), pp. 1505–1513. doi: https://doi.org/10.1109/TFUZZ.2009.2033792
[26] Zhang, Y., Naidu, D.S., Cai, C. and Zou, Y., 2016. Composite control of a class of nonlinear
singularly perturbed discretetime systems via DSDRE. Int. J. Syst. Sci., 47(11), pp. 2632–2641.
doi: https://doi.org/10.1080/00207721.2015.1006710
[27] Zhao, J.Y., 1990. Iterative Determination of Analytical Quasioptimal Control for Nonlinear
Discretetime Systems . France: PhD Thesis.
)