Robust ISS of uncertain discrete-time singularly perturbed systems with disturbances

References

• Boyd, S., Ghaoui, L. E. E., Feron, E., & Balakrishnan, V. (1994). Linear matrix inequalities in system and control theory. Philadelphia, PA: Siam.
   Google Scholar
• Cassandras, C. G. (2014). The event-driven paradigm for control, communication and optimization. Journal of Control and Decision, 1(1), 3–17. doi: 10.1080/23307706.2014.885288
   Google Scholar
• Chen, B. S., & Lin, C. L. (1990). On the stability bounds of singularly perturbed systems. Transactions on Automatic Control, 35(11), 1265–1270. doi: 10.1109/9.59817
   Web of Science ®Google Scholar
• Cui, Y. K., Lam, J., Feng, Z. G., & Shen, J. (2016). Robust admissibility and admissibilisation of uncertain discrete time-delay systems. International Journal of Systems Science, 47(15), 3720–3729. doi: 10.1080/00207721.2015.1117158
   Web of Science ®Google Scholar
• Dong, J., & Yang, G. H. (2007). Robust H∞ control for standard discrete-time singularly perturbed systems. IET Control Theory & Applications, 1(4), 1141–1148. doi: 10.1049/iet-cta:20060234
   Web of Science ®Google Scholar
• Dong, J., & Yang, G. H. (2008). H∞ control for fast sampling discrete-time singularly perturbed systems. Automatica, 44(5), 1385–1393. doi: 10.1016/j.automatica.2007.10.010
   Web of Science ®Google Scholar
• Esfandiari, K., Abdollahi, F., & Talebi, H. A. (2015). Adaptive control of uncertain non-affine non-linear systems with input saturation using neural networks. IEE Transactions of Neural Network and Learning Systems, 26(10), 2311–2322. doi: 10.1109/TNNLS.2014.2378991
   PubMed Web of Science ®Google Scholar
• Freeman, R. A., & Kokotovic, P. V. (1996). Robust nonlinear control design: State-space and Lyapunov techniques. Boston: Birkhauser.
   Google Scholar
• Fu, Z. J., Xie, W. F., & Luo, W. D. (2013). Robust on-line nonlinear systems identification using multilayer dynamical neural networks with two time scales. Neurocomputing, 113, 16–26. doi: 10.1016/j.neucom.2012.11.041
   Web of Science ®Google Scholar
• Ge, S. S., Lee, T. H., & Wang, Z. P. (2001). Adaptive neural network control for smart materials robots using singular perturbation technique. Asian Journal of Control, 3(2), 143–155. doi: 10.1111/j.1934-6093.2001.tb00053.x
   Google Scholar
• Ghosh, R., Sen, S., & Datta, K. B. (1999). Method for evaluating stability bounds for discrete-time singularly perturbed systems. IEE Proceedings-Control Theory and Applications, 146(2), 227–233. doi: 10.1049/ip-cta:19990166
   Google Scholar
• Glizer, V. Y., & Kelis, O. (2015). Solution of a zero-sum linear quadratic differential game with singular control cost of minimiser. Journal of Control and Decision, 2(3), 155–184. doi: 10.1080/23307706.2015.1057545
   Google Scholar
• Jiang, Z. P., Teel, A. R., & Praly, L. (1994). Small-gain theorem for ISS systems and applications. Mathematics of Control, Signals and Systems, 7(2), 95–120. doi: 10.1007/BF01211469
   Web of Science ®Google Scholar
• Jiang, Z. P., & Wang, Y. (2001). Input-to-state stability for discrete-time nonlinear systems. Automatica, 37(6), 857–869. doi: 10.1016/S0005-1098(01)00028-0
   Web of Science ®Google Scholar
• Kafri, W. S., & Abed, E. H. (1996). Stability analysis of discrete time singularly perturbed systems. IEEE Transactions on Circuits and Systems, 43(10), 848–850. doi: 10.1109/81.538991
   Google Scholar
• Kokotovic, P. V. (1984). Applications of singular perturbation techniques to control problems. SIAM Reviews, 26(4), 501–550. doi: 10.1137/1026104
   Web of Science ®Google Scholar
• Kokotovic, P. V., Khalil, H. K., & O’Reilly, J. (1986). Singular perturbation methods in control: Analysis and design. London: Academic Press.
   Google Scholar
• Kokotovic, P. V., O’Malley, R. E., & Sannuti, P. (1976). Singular perturbation and order reduction in control theory: An overview. Automatica, 12(2), 123–132. doi: 10.1016/0005-1098(76)90076-5
   Web of Science ®Google Scholar
• Li, T. S., & Li, J. (1992). Stabilization bound of discrete two-time-scale systems. System and Control Letters, 18(6), 479–489. doi: 10.1016/0167-6911(92)90052-T
   Web of Science ®Google Scholar
• Li, X. J., & Yang, G. H. (2016). FLS-based adaptive synchronization control of complex dynamical networks with nonlinear couplings and state-dependent uncertainties. IEEE Transactions on Cybernetics, 46(1), 171–180. doi: 10.1109/TCYB.2015.2399334
   PubMed Web of Science ®Google Scholar
• Li, X. J., & Yang, G. H. (2017). Fuzzy approximation-based global pinning synchronization control of uncertain complex dynamical networks. IEEE Transactions on Cybernetics, 47(4), 873–883. doi: 10.1109/TCYB.2016.2530792
   PubMed Web of Science ®Google Scholar
• Litkouhi, B., & Khalil, H. K. (1985). Multirate and composite control of two-time-scale discrete-time systems. IEEE Transactions on Automatic Control, 30(7), 645–651. doi: 10.1109/TAC.1985.1104024
   Web of Science ®Google Scholar
• Liu, W., & Wang, Y. Y. (2017). Robustness of proper dynamic output feedback for discrete-time singularly perturbed systems. Advances in Difference Equations, 2017(384), 1–12.
   Google Scholar
• Liu, W., Wang, Z. M., Dai, H. H., & Mehvish, N. (2016). Dynamic output feedback control for fast sampling discrete-time singularly perturbed systems. IET Control Theory &Applications, 10(15), 1782–1788. doi: 10.1049/iet-cta.2016.0121
   Web of Science ®Google Scholar
• Naidu, D. S. (1988). Singular perturbation methodology in control systems. London: Peter Peregrinus.
   Google Scholar
• Naidu, D. S., & Rao, A. K. (1985). Singular perturbation analysis of discrete control systems. New York, NY: Springer- Verlag.
   Google Scholar
• Pan, Y. N., & Yang, G. H. (2017). Event-triggered fuzzy control for nonlinear networked control systems. Fuzzy Sets and Systems, 329, 91–107. doi: 10.1016/j.fss.2017.05.010
   Web of Science ®Google Scholar
• Pan, Y. N., & Yang, G. H. (2018). Event-triggered fault detection filter design for nonlinear networked systems. IEEE Transactions on Systems, Man, and Cybernetics; Systems, 48(11), 1851–1862. doi: 10.1109/TSMC.2017.2719629
   Web of Science ®Google Scholar
• Shao, Z. (2004). Stability bounds of singularly perturbed delay systems. IEE Proc., Control Theory Appl, 151(4), 585–588. doi: 10.1049/ip-cta:20040927
   Google Scholar
• Shi, P., & Dragan, V. (1997). H∞ control for singularly perturbed systems with parametric uncertainties. American control conference, IEEE. 0743-1619.
   Google Scholar
• Singh, H., Brown, R. H., Naidu, D. S., & Heinen, J. A. (2001). Robust stability of singularly perturbed state feedback systems using unified approach. IEE Proceedings-Control Theory and Applications, 148(5), 391–396. doi: 10.1049/ip-cta:20010681
   Google Scholar
• Sontag, E. D. (1989). Smooth stabilization implies coprime factorization. IEEE Transactions on Automatic Control, 34(4), 435–443. doi: 10.1109/9.28018
   Web of Science ®Google Scholar
• Sontag, E. D. (1990). Further facts about input to state stabilization. IEEE Trans. Automatic Control, 35(4), 473–476. doi: 10.1109/9.52307
   Web of Science ®Google Scholar
• Sontag, E. D., & Teel, A. R. (1995). Changing supply function in input/state stable systems. IEEE Transactions on Automatic Control, 40(8), 1476–1478. doi: 10.1109/9.402246
   Web of Science ®Google Scholar
• Sun, F., Hu, Y., & Liu, H. (2005). Stability analysis and robust controller design for uncertain discrete-time singularly perturbed systems. Dynamics of Continuous Discrete & Impulsive Systems Series B: Applications & Algorithms, 12(5–6), 849–865.
   Google Scholar
• Teel, A. R., Moreau, L., & Nesic, D. (2003). A unified framework for input-to-state stability in systems with two time scales. IEEE Transactions on Automatic Control, 48(9), 1526–1544. doi: 10.1109/TAC.2003.816966
   Web of Science ®Google Scholar
• Xu, J., Cai, C. X., & Zou, Y. (2015). Composite state feedback of the Finite frequency H-infinity control for discrete-time singularly perturbed systems. Asian Journal of Control, 17(6), 2188–2205. doi: 10.1002/asjc.1118
   Web of Science ®Google Scholar
• Xu, S., & Feng, G. (2009). New results on H∞ control of discrete singularly perturbed systems. Automatica, 45(10), 2339–2343. doi: 10.1016/j.automatica.2009.06.011
   Web of Science ®Google Scholar
• Yang, C. Y., & Zhou, L. N. (2015). H∞ control and ε-bound estimation of discrete-time singularly perurbed systems. Circuits. Systems, and Signal Process, 35(7), 2640–2654. doi: 10.1007/s00034-015-0165-7
   Web of Science ®Google Scholar
• Yin, S., Yang, H., Gao, H., Qui, J., & Kayank, O. (2017). An adaptive NN-based approach for fault tolerant control of nonlinear time-varying delay systems with unmodeled dynamics. IEEE Transactions of Neural Networks and Learning Systems, 28(8), 1902–1913. doi: 10.1109/TNNLS.2016.2558195
   PubMed Web of Science ®Google Scholar
• Yu, H. W., Lu, G. P., & Zheng, Y. F. (2011). On the model-based networked control for singularly perturbed systems with nonlinear uncertainties. Systems and Control Letters, 60(9), 739–746. doi: 10.1016/j.sysconle.2011.05.012
   Web of Science ®Google Scholar
• Yuan, L., Achenie, L. E. K., & Jiang, W. (1997). Robust H∞ control for linear discrete-time systems with norm bounded time-varying uncertainties. Systems and Control Letters, 27(4), 199–208. doi: 10.1016/0167-6911(95)00049-6
   Web of Science ®Google Scholar
• Zhang, Y., Naidu, D. S., Cai, C. X., & Zou, Y. (2016). Composite control of a class of nonlinear singularly perturbed discrete-time systems via D-SDRE. International Journal of Systems Science, 47(11), 2632–2641. doi: 10.1080/00207721.2015.1006710
   Web of Science ®Google Scholar