Abstract
The robust finite-time \(H_{\infty }\) control for a kind of uncertain delay systems with large delay period (LDP) is discussed in this paper. First, a switching technique is exploited to transform the original system into a switched delay system. Second, within the limitation of frequency and length rate of LDP, a state feedback controller is designed to guarantee that the closed-loop system is robust finite-time bounded. Third, the finite-time \(H_{\infty }\) performance analysis for the closed-loop system is developed. Finally, two examples are presented to clarify the validity of the proposed approach.
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F. Amato, M. Ariola, P. Dorato, Finite-time control of linear systems subject to parameteric uncertainties and disturbances. Automatica 37(9), 1459–1463 (2001)
X.W. Chen, S.L. Du, L.D. Wang, L.J. Liu, Stabilization for linear uncertain systems with switched time-varying delays. Neurocomputing 191, 296–303 (2016)
P. Dorato, Short time stability in linear time-varying systems, in Proceedings of the IRE International Convention Record Part 4, New York, pp. 83-87 (1961)
S.L. Du, R. Wang, S. Wang, M. Yu, Observer-based \(H_{\infty }\) stabilisation for linear systems with large delay periods. IET Control Theory Appl. 10(4), 417–423 (2016)
H. Fang, Z. Lin, Stability analysis for linear systems under state constraints. IEEE Trans. Autom. Control 49(6), 950–955 (2004)
T.T. Guo, B.W. Wu, Y.E. Wang, Stability and \(L_{1}\)-gain analysis for positive delay systems with large delay period. Trans. Inst. Meas. Control. (2017). https://doi.org/10.1177/0142331217731622
H.T.M. Kussaba, R.A. Borges, J.Y. Ishihara, A new condition for finite time boundedness analysis. J. Frankl. Inst. 352(12), 5514–5528 (2015)
O. Kwon, J.H. Park, On improve delay-dependent robust control for uncertain time-delay systems. IEEE Trans. Autom. Control 49(11), 1991–1995 (2004)
H.J. Liang, H.Y. Li, Z.D. Yu, P. Li, W. Wang, Cooperative robust containment control for general discrete-time multi-agent systems with external disturbance. IET Control Theory Appl. 11(12), 1928–1937 (2017)
X.Z. Lin, H.B. Du, S.H. Li, Y. Zou, Finite-time stability and finite-time weighted \(L_{2}\)-gain analysis for switched systems with time-varying delay. IET Control Theory Appl. 7(7), 1058–1069 (2013)
X.Z. Lin, H.B. Du, S.H. Li, Finite-time boundedness and \(L_{2}\)-gain analysis for switched delay systems with norm-bounded disturbance. Appl. Math. Comput. 217(12), 5982–5993 (2011)
X.G. Lin, K. Liang, H. Li, Y.Z. Jiao, J. Nie, Finite-time stability and stabilization for continuous systems with additive time-varying delays. Circuits Syst. Signal Process. 36(7), 2971–2990 (2017)
H. Liu, Y. Shen, Asynchronous finite-time stabilisation of switched systems with average dwell time. IET Control Theory Appl. 6(9), 1213–1219 (2012)
B. Niu, C.K. Ahn, H. Li, M. Liu, Adaptive control for stochastic switched nonlower triangular nonlinear systems and its application to a one-link manipulator. IEEE Trans. Syste. Man Cybern. Syst. PP(99), 1–14 (2017)
B. Niu, L. Li, Adaptive backstepping-based neural tracking control for MIMO nonlinear switched systems subject to input delays. IEEE Trans. Neural Netw. Learn. Syst. PP(99), 1–7 (2017)
B. Niu, Y.J. Liu, G.D. Zong, Z.Y. Han, J. Fu, Command filter-based adaptive neural tracking controller design for uncertain switched nonlinear output-constrained systems. IEEE Trans. Cybern. PP(99), 1–12 (2017)
I.R. Petersen, C.V. Hollot, A Riccati equation approach to the stabilization of uncertain linear systems. Automatica 22(4), 397–411 (1986)
S.B. Stojanovic, D.L. Debeljkovic, D.S. Antic, Robust finite-time stability and stabilization of linear uncertain time-delay systems. Asian J. Control 15(5), 1548–1554 (2013)
P. Shi, X. Su, F. Li, Dissipativity-based filtering for fuzzy switched systems with stochastic perturbation. IEEE Trans. Autom. Control 61(6), 1694–1699 (2016)
P. Shi, Y.Q. Zhang, R.K. Agarwald, Stochastic finite-time state estimation for discrete time-delay neural networks with Markovian jumps. Neurocomputing 151(1), 168–174 (2015)
X.M. Sun, G.P. Liu, D. Rees, W. Wang, Delay-dependent stability for discrete systems with large delay sequence based on switching techniques. Automatica 44, 2902–2908 (2008)
X.M. Sun, G.P. Liu, W. Wang, D. Rees, Stability analysis for systems with large delay period: a switching method. Int. J. Innov. Comput. Inf. Control 8(6), 4235–4247 (2012)
X.M. Sun, L.D. Wang, W. Wang, G.Z. Tan, Input-to-state stability for nonlinear systems with large delay period based on switching techniques. Chin. Control Decis. Conf. 61(6), 288–291 (2013)
A. Ucar, A prototype model for chaos studies. Int. J. Eng. Sci. 40(3), 251–258 (2002)
A. Ucar, On the chaotic behavior of a prototype delays dynamical system. Chaos Solitons Fractals 16(2), 187–194 (2003)
J.W. Wen, S.K. Nguang, P. Shi, L. Peng, Finite-time stabilization of Markovian jump delay systems—a switching control approach. Int. J. Robust Nonlinear Control 27(2), 298–318 (2017)
Y.E. Wang, X.M. Sun, F. Mazenc, Stability of switched nonlinear systems with delay and disturbance. Automatica 69(C), 78–86 (2016)
Y.E. Wang, X.M. Sun, B.W. Wu, Lyapunov–Krasovskii functionals for input-to-state stability of switched non-linear systems with time-varying input delay. IET Control Theory Appl. 9(11), 1717–1722 (2015)
T. Wang, Q. Wang, L. Wei, C.Y. Dong, Finite-time \(H_{\infty }\) control for switched linear systems based on mode-dependent average dwell time. Control Decis. 30(7), 1189–1194 (2015)
R. Wang, Y.T. Sun, P. Shi, S.N. Wu, Exponential stability of descriptor systems with large delay period based on a switching method. Inf. Sci. 286, 147–160 (2014)
R. Wang, P. Shi, Z.G. Wu, Y.T. Sun, Stabilization of switched delay systems with polytopic uncertainties under asynchronous switching. J. Frankl. Inst. 350(8), 2028–2043 (2013)
Z.R. Xiang, Y.N. Sun, M.S. Mahmoud, Robust finite-time \(H_{\infty }\) control for a class of uncertain switched neutral systems. Commun. Nonlinear Sci. Numer. Simul. 17(4), 1766–1778 (2012)
F. Yang, H. Zhang, Delay dependent stability conditions of static recurrent neural networks: a nonlinear convex combination method. IET Control Theory Appl. 8(14), 1396–1404 (2014)
F. Yang, J. He, D. Wang, New stability criteria of delayed load frequency control systems via infinite-series-based inequality. IEEE Trans. Ind. Inform. (2017). https://doi.org/10.1109/TII.2017.2751510
X. Zhao, L.X. Zhang, P. Shi, M. Liu, Stability and stabilization of switched linear systems with mode-dependent average dwell time. IEEE Trans. Autom. Control 57(7), 1809–1815 (2012)
B. Zhou, On asymptotic stability of linear time-varying systems. Automatica 68, 266–276 (2016)
J.L. Zhang, H. Zhang, T. Feng, Distributed optimal consensus control for nonlinear multi-agent system with unknown dynamic. IEEE Trans. Neural Netw. Learn. Syst. (2017). https://doi.org/10.1109/TNNLS.2017.2728622
Acknowledgements
The work was supported by the National Natural Science Foundation of China under Grants 61403241, 11371233, the Fundamental Research Funds for the Central Universities under Grant GK201703009, and the scientific and technological innovation programs of higher education institutions in Shanxi (2017149).
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Guo, T., Wu, B., Wang, YE. et al. Delay-Dependent Robust Finite-Time \(H_{\infty }\) Control for Uncertain Large Delay Systems Based on a Switching Method. Circuits Syst Signal Process 37, 4753–4772 (2018). https://doi.org/10.1007/s00034-018-0799-3
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DOI: https://doi.org/10.1007/s00034-018-0799-3