Xinyue Tang
School of Mathematical Sciences, Tiangong University, Tianjin, 300387, China
Yali Dong
School of Mathematical Sciences, Tiangong University, Tianjin, 300387, China
Meng Liu
School of Mathematical Sciences, Tiangong University, Tianjin, 300387, China
This paper investigates the finite-time H∞ control problem for a class of nonlinear discrete-time one-sided Lipschitz systems with uncertainties. Using the one-sided Lipschitz and quadratically inner-bounded conditions, the authors derive less conservative criterion for the controller design and observer design. A new criterion is proposed to ensure the closedloop system is finite-time bounded (FTB). The sufficient conditions are established to ensure the closed-loop system is H∞ finite-time bounded (H∞ FTB) in terms of matrix inequalities. The controller gains and observer gains are given. A numerical example is provided to demonstrate the effectiveness of the proposed results.
[1] Dong, H.L., Wang, Z.D., Gao, H.D., 2010. Observer-based H∞ control for systems with repeated scalar nonlinearities and multiple packet losses. International Journal of Robust and Nonlinear Control. 20(12), 1363-1378.
[2] Wang, W., Ma, S.P., Zhang, C.H., 2013. Stability and static output feedback stabilization for a class of non-linear discrete-time singular switched systems. International Journal of Control Automation and Systems. 11(6), 1138-1148.
[3] Wang, J.M., Ma, S.P., Zhang, C.H., 2017. Finite-time stabilization for nonlinear discrete-time singular Markov jump systems with piecewise-constant transition probabilities subject to average dwell time. Journal of the Franklin Institute. 354(5), 2102-2124.
[4] Wang, J.M., Ma, S.P., Zhang, C.H., 2016. Stability analysis and stabilization for nonlinear continuous-time descriptor semi-Markov jump systems. Applied Mathematics and Computation. 279, 90-102.
[5] Abbaszadeh, M., Marquez, H., 2010. Nonlinear observer design for one-sided Lipschitz systems. American Control Conference. pp. 5284-5289.
[6] Du, Z.P., Yuan, W.R., Hu, S.L., 2019. Discrete-time event triggered H-infinity stabilization for networked cascade control systems with uncertain delay. Journal of the Franklin Institute Engineering and Applied Mathematics. 356(16), 9524-9544.
[7] Song, Y., Fan, J., Fei, M.R., et al., 2008. Robust H∞ control of discrete switched system with time delay. Applied Mathematics and Computation. 205(1), 159- 169.
[8] Wang, R., Wang, B., Liu, G.P., et al., 2010. H∞ controller design for networked predictive control systems based on the average dwell-time approach. IEEE Transactions on Circuits and Systems. 579(4), 310-314.
[9] Chen, H.F., Gao, J.F., Shi, T., et al., 2016. H∞ control for networked control systems with time delay, data packet dropout and disorder. Neurocomputing. 179(29), 211-218.
[10] Chang, X.H., Yang, G.H., 2014. New results on output feedback H∞ control for linear discrete-time systems. IEEE Transactions on Automatic Control. 59(5), 1355-1359.
[11] Chang, X.H., Zhang, L., Park, J.H., 2015. Robust static output feedback H∞ control for uncertain fuzzy systems. Fuzzy Sets and Systems. 273(15), 87-104.
[12] Miao, X.F., Xu, Y.Q., Yao, F.G., 2021. Observers design for a class of nonlinear stochastic discrete-time systems. International Journal of Theoretical Physics. 60(7), 26042612.
[13] Badreddine, E., Hicham, E., Abdelaziz, H., et al., 2019. New approach to robust observer-based control of one-sided Lipschitz non-linear systems. IET Control Theory and Applications. 13(3), 333-342.
[14] Dong, H.L., Wang. Z.D., Gao, H.J., 2010. Observer-based H∞ control for systems with repeated scalar nonlinearities and multiple packet losses. International Journal of Robust and Nonlinear Control. 20, 1363-1378.
[15] Wang, J.X., Wu, H.C., Ji, X.F., et al., 2020. Robust finite-time stabilization for uncertain discrete-time linear singular systems. IEEE Access. 8, 100645- 100651.
[16] Feng, T., Wu, B.W., Liu, L.L., et al., 2019. Finite time stability and stabilization of fractional- order switched singular continuous-time system. Circuits Systems and Signal Processing. 38(12), 5528-5548.
[17] Zhang, T.L., Deng, F.Q., Zhang, W.H., 2019. Finite-time stability and stabilization of linear discrete time-varying stochastic systems. Journal of the Franklin Institute Engineering and Applied Mathematics. 356(3), 1247-1267.
[18] Ban, J., Kwon, W., Won, S., et al., 2018. Robust H∞ finite-time control for discrete- time polytopic uncertain switched linear systems. Nonlinear Analysis-Hybrid Systems. 29, 348-362.
[19] Benallouch, M., Boutayeb, M., Zasadzinski, M., 2012. Observer design for one-sided Lipschitz discrete-time systems. Systems and Control Letters. 61(9), 879-886.
Copyright © 2022 Author(s)
This is an open access article under the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) License.
