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Robust H Control of Switched Nonlinear Systems Under Sampled Data

ZHAO Hongpeng, WANG Xingtao   

  1. School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
  • Received:2021-02-23 Revised:2021-03-28 Online:2022-10-25 Published:2022-10-12

ZHAO Hongpeng, WANG Xingtao. Robust H Control of Switched Nonlinear Systems Under Sampled Data[J]. Journal of Systems Science and Complexity, 2022, 35(5): 1785-1807.

This paper investigates the globally asymptotically stable and L2-gain of robust H control for switched nonlinear systems under sampled data.By considering the relationship between the sampling period and the dwell time,the non-switching and one switching are discussed in the sampling interval,respectively.Firstly,a state feedback sampled-data controller is constructed by the back-stepping method,and the switching converts to asynchronous switching if it happens within the sampling interval.Then,under the limiting conditions of the sampling period,which are obtained by the average dwell time method,the closed-loop system is globally asymptotically stable and has L2-gain.Finally,two numerical examples are provided to demonstrate the effectiveness of the proposed method.
[1] Ma J, Hong N, Jie X, et al., Deterministic sampling strong tracking filtering algorithms:Fast detection and isolation for aircraft actuator fault, Control Theory and Applications, 2015, 32:734-743.
[2] Liu Z, Wang L, Wang J, et al., Distributed sampled-data control of nonholonomic multi-robot systems with proximity networks, Automatica, 2017, 77(6):170-179.
[3] Wang L and Liu X, Robust H∞ fuzzy output feedback control for uncertain discrete-time nonlinear systems, Internationa Journal of Fuzzy Systems, 2010, 12(3):218-226.
[4] Gao J and Wang X, Asynchronous H∞ control of switched systems with mode-dependent average dwell time, Circuits Systems and Signal Processing, 2017, 36(11):4401-4422.
[5] Niamsup P and Phat V, Robust finite-time H∞ control of linear time-varying delay systems with bounded control via riccati equations, International Journal of Automation and Computing, 2018, 15(3):109-117.
[6] Ren J, He Gu, and Fu J, Robust H∞ sliding mode control for nonlinear stochastic T-S fuzzy singular markovian jump systems with time-varying delays, Information Sciences, 2020, 535:42-63.
[7] Lee D, Joo Y, and Kim S, H∞ digital redesign for LTI systems, International Journal of Control Automation and Systems, 2015, 13(3):603-610.
[8] Fridman E, Shaked U, and Suplin V, Input/output delay approach to robust sampled-data H∞ control, Systems and Control Letters, 2005, 54(3):271-282.
[9] Shao H, Han Q, Zhang Z, et al., Sampling-interval-dependent stability for sampled-data systems with state quantization, International Journal of Robust and Nonlinear Control, 2013, 24(17):2995-3008.
[10] Gao H, Wu J, and Peng S, Robust sampled-data control with stochastic sampling, Automatica, 2009, 45(7):1729-1736.
[11] Wen S and Zeng Z, Robust sampled-data H∞ output tracking control for a class of nonlinear networked systems with stochastic sampling, International Journal of Systems Science, 2012, 44(9):1-13.
[12] Ding Z, Xi C, An L, et al., Prescribed performance switched adaptive dynamic surface control of switched nonlinear systems with average dwell time, IEEE Transactions on Systems Man and Cybernetics Systems, 2017, 47(7):1257-1269.
[13] Yazdi M and Jahed-Motlagh M, Stabilization of a CSTR with two arbitrarily switching modes using modal state feedback linearization, Chemical Engineering Journal, 2009, 155(3):838-843.
[14] Pang H and Liu S, Robust exponential quasi passivity and global stabilization for uncertain switched nonlinear systems, International Journal of Robust and Nonlinear Control, 2020, 30(18):8117-8138.
[15] Korobov V and Pavlichkov S, Global properties of the triangular systems in the singular case, Journal of Mathematical Analysis and Applications, 2008, 342(2):1426-1439.
[16] Chang X, Ju H, and Zhou J, Robust static output feedback H∞ control design for linear systems with polytopic uncertainties, Systems and Control Letters, 2015, 85:23-32.
[17] Li Z and Chang X, Robust H∞ control for networked control systems with randomly occurring uncertainties:Observer-based case, ISA Transactions, 2018, 83:13-24.
[18] Tang L and Zhao J, Neural network based adaptive prescribed performance control for a class of switched nonlinear systems, Neurocomputing, 2017, 230:316-321.
[19] Li Y, Tong S, Liu L, et al., Adaptive output-feedback control design with prescribed performance for switched nonlinear systems, Automatica, 2017, 80:225-231.
[20] Lai G, Liu Z, Zhang Y, et al., Adaptive backstepping-based tracking control of a class of uncertain switched nonlinear systems, Automatica, 2018, 91:301-310.
[21] Niu B, Karimi H, Wang H, et al., Adaptive output-feedback controller design for switched nonlinear stochastic systems with a modified average dwell-time method, IEEE Transactions on Systems Man and Cybernetics Systems, 2017, 47(7):1371-1382.
[22] Zhang X, Lin A, and Zeng J, Exponential stability of nonlinear impulsive switched systems with stable and unstable subsystems, Frontiers of Information Technology and Electronic Engineering, 2014, 15(1):31-42.
[23] Long L, Multiple Lyapunov functions-based small-gain theorems for switched interconnected nonlinear systems, IEEE Transactions on Automatic Control, 2017, 62(8):3943-3958.
[24] Niu B and Zhao J, Robust stabilization and tracking control for a class of switched nonlinear systems, Asian Journal of Control, 2013, 15(5):1496-1502.
[25] Wang Y, Niu B, Wang H, et al., Neural network-based adaptive tracking control for switched nonlinear systems with prescribed performance:An average dwell time switching approach, Neurocomputing, 2020, 435(6):295-306.
[26] Chang Y, Zhang S, Alotaibi N, et al., Observer-based adaptive finite-time tracking control for a class of switched nonlinear systems with unmodeled dynamics, IEEE Access, 2020, 8:204782-204790.
[27] Wang Y, Xu N, Liu Y, et al., Adaptive fault-tolerant control for switched nonlinear systems based on command filter technique, Applied Mathematics and Computation, 2021, 392:1-18.
[28] Li S, Guo J, and Xiang Z, Global stabilization of a class of switched nonlinear systems under sampled-data control, IEEE Transactions on Systems Man and Cybernetics Systems, 2019, 49(9):1912-1919.
[29] Hetel L and Fridman E, Robust sampled-data control of switched affine system, IEEE Transactions on Automatic Control, 2013, 58(11):2922-2928.
[30] Hauroigne P, Riedinger P, and Iung C, Switched affine systems using sampled-data controllers:Robust and guaranteed stabilization, IEEE Transactions on Automatic Control, 2011, 56(12):2929-2935.
[31] Mao J, Xiang Z, and Zhai G, Sampled-data output feedback stabilization for a class of switched stochastic nonlinear systems, International Journal of Robust and Nonlinear Control, 2019, 29(10):2844-2861.
[32] Li S and Xiang Z, Sampled-data decentralized output feedback control for a class of switched large-scale stochastic nonlinear systems, IEEE Systems Journal, 2020, 14(2):1602-1610.
[33] Qian C and Wei L, Almost disturbance decoupling for a class of high-order nonlinear systems, Mathematics in Practice and Theory, 2000, 45(6):1208-1214.
[34] Liberzon D, Switching in Systems and Control, Springer, New York, 2003.
[35] Bi W, Robust H∞ control for uncertain nonlinear systems, Journal of Systems Science&Complexity, 2007, 20(4):545-553.
[36] Apostol T, Mathematical Analysis, 2nd Edition, Addison-Wesley Pub. Co, Boston, 1974.
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