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Finite-time stability of large-scale systems with interval time-varying delay in interconnection. (English) Zbl 1367.93439

Summary: We investigate finite-time stability of a class of nonlinear large-scale systems with interval time-varying delays in interconnection. Time-delay functions are continuous but not necessarily differentiable. Based on Lyapunov stability theory and new integral bounding technique, finite-time stability of large-scale systems with interval time-varying delays in interconnection is derived. The finite-time stability criteria are delays-dependent and are given in terms of linear matrix inequalities which can be solved by various available algorithms. Numerical examples are given to illustrate effectiveness of the proposed method.

MSC:

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93A15 Large-scale systems
93C10 Nonlinear systems in control theory
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[1] Botmart, T.; Niamsup, P.; Phat, V. N., Delay-dependent exponential stabilization for uncertain linear systems with interval non-differentiable time-varying delays, Applied Mathematics and Computation, 217, 21, 8236-8247 (2011) · Zbl 1241.34080
[2] Liu, J.; Liu, X.; Xie, W.-C., Delay-dependent robust control for uncertain switched systems with time-delay, Nonlinear Analysis: Hybrid Systems, 2, 1, 81-95 (2008) · Zbl 1157.93362
[3] Wang, D.; Wang, W., Delay-dependent robust exponential stabilization for uncertain systems with interval time-varying delays, Journal of Control Theory and Applications, 7, 3, 257-263 (2009)
[4] Zhang, W.; Cai, X.-S.; Han, Z.-Z., Robust stability criteria for systems with interval time-varying delay and nonlinear perturbations, Journal of Computational and Applied Mathematics, 234, 1, 174-180 (2010) · Zbl 1185.93111
[5] Zhao, X.; Zhang, L.; Shi, P., Stability of a class of switched positive linear time-delay systems, International Journal of Robust and Nonlinear Control, 23, 5, 578-589 (2013) · Zbl 1284.93208
[6] Jeong, C.; Park, P.; Kim, S. H., Improved approach to robust stability and \(H_\infty\) performance analysis for systems with an interval time-varying delay, Applied Mathematics and Computation, 218, 21, 10533-10541 (2012) · Zbl 1253.93103
[7] Zhang, B.; Lam, J.; Xu, S., Relaxed results on reachable set estimation of time-delay systems with bounded peak inputs, International Journal of Robust and Nonlinear Control, 26, 9, 1994-2007 (2016) · Zbl 1342.93021
[8] Kwon, O. M.; Park, M. J.; Park, J. H.; Lee, S. M.; Cha, E. J., Improved approaches to stability criteria for neural networks with time-varying delays, Journal of the Franklin Institute. Engineering and Applied Mathematics, 350, 9, 2710-2735 (2013) · Zbl 1287.93073
[9] Lee, W. I.; Lee, S. Y.; Park, P.; Lee, S., Improved criteria on robust stability and performance analysis for systems with interval time-varying delay via new triple integral functionals, Applied Mathematics and Computation, 243, 570-577 (2014) · Zbl 1335.93096
[10] Park, P.; Ko, J. W.; Jeong, C., Reciprocally convex approach to stability of systems with time-varying delays, Automatica, 47, 1, 235-238 (2011) · Zbl 1209.93076
[11] Zhang, X.-M.; Han, Q.-L., Novel delay-derivative-dependent stability criteria using new bounding techniques, International Journal of Robust and Nonlinear Control, 23, 13, 1419-1432 (2013) · Zbl 1278.93230
[12] He, Y.; Wang, Q.-G.; Lin, C.; Wu, M., Delay-range-dependent stability for systems with time-varying delay, Automatica, 43, 2, 371-376 (2007) · Zbl 1111.93073
[13] Yue, D.; Han, Q.-L.; Lam, J., Network-based robust \(\text{H}_\infty\) control of systems with uncertainty, Automatica, 41, 6, 999-1007 (2005) · Zbl 1091.93007
[14] Seuret, A.; Gouaisbaut, F., Wirtinger-based integral inequality: application to time-delay systems, Automatica, 49, 9, 2860-2866 (2013) · Zbl 1364.93740
[15] Park, P.; Lee, W. I.; Lee, S. Y., Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems, Journal of the Franklin Institute, 352, 4, 1378-1396 (2015) · Zbl 1395.93450
[16] Hien, L. V.; Trinh, H., An enhanced stability criterion for time-delay systems via a new bounding technique, Journal of the Franklin Institute. Engineering and Applied Mathematics, 352, 10, 4407-4422 (2015) · Zbl 1395.93443
[17] Hien, L. V.; Trinh, H., Refined Jensen-based inequality approach to stability analysis of time-delay systems, IET Control Theory & Applications, 9, 14, 2188-2194 (2015)
[18] Liu, Y.; Lee, S. M.; Kwon, O. M.; Park, J. H., New approach to stability criteria for generalized neural networks with interval time-varying delays, Neurocomputing, 149, 1544-1551 (2015)
[19] Fernando, T. L.; Phat, V. N.; Trinh, H. M., Decentralized stabilization of large-scale systems with interval time-varying delays in interconnections, International Journal of Adaptive Control and Signal Processing, 26, 6, 541-554 (2012) · Zbl 1263.93192
[20] Hua, C.-C.; Leng, J.; Guan, X.-P., Decentralized MRAC for large-scale interconnected systems with time-varying delays and applications to chemical reactor systems, Journal of Process Control, 22, 10, 1985-1996 (2012)
[21] Liu, X.; Zhang, H., Delay-dependent robust stability of uncertain fuzzy large-scale systems with time-varying delays, Automatica, 44, 1, 193-198 (2008) · Zbl 1138.93394
[22] Phat, V. N.; Thanh, N. T.; Trinh, H., Full-order observer design for nonlinear complex large-scale systems with unknown time-varying delayed interactions, Complexity, 21, 2, 123-133 (2015)
[23] Thanh, N. T.; Phat, V. N., Decentralized stability for switched nonlinear large-scale systems with interval time-varying delays in interconnections, Nonlinear Analysis: Hybrid Systems, 11, 22-36 (2014) · Zbl 1298.34137
[24] Yoo, S. J.; Park, J. B., Decentralized adaptive output-feedback control for a class of nonlinear large-scale systems with unknown time-varying delayed interactions, Information Sciences, 186, 222-238 (2012) · Zbl 1401.93018
[25] Zhao, X.; Yang, H.; Karimi, H. R.; Zhu, Y., Adaptive neural control of MIMO nonstrict-feedback nonlinear systems with time delay, IEEE Transactions on Cybernetics, 46, 6, 1337-1349 (2015)
[26] Liu, H.; Shen, Y.; Zhao, X., Asynchronous finite-time \(H_\infty\) control for switched linear systems via mode-dependent dynamic state-feedback, Nonlinear Analysis. Hybrid Systems. An International Multidisciplinary Journal, 8, 109-120 (2013) · Zbl 1258.93055
[27] Chen, G.; Yang, Y., Finite-time stability of switched positive linear systems, International Journal of Robust and Nonlinear Control, 24, 1, 179-190 (2012) · Zbl 1278.93229
[28] Liu, H.; Shen, Y.; Zhao, X., Finite-time stabilization and boundedness of switched linear system under state-dependent switching, Journal of the Franklin Institute, 350, 3, 541-555 (2013) · Zbl 1268.93078
[29] Niamsup, P.; Ratchagit, K.; Phat, V. N., Novel criteria for finite-time stabilization and guaranteed cost control of delayed neural networks, Neurocomputing, 160, 281-286 (2015)
[30] Shi, K.; Zhong, S.; Zhu, H.; Liu, X.; Zeng, Y., New delay-dependent stability criteria for neutral-type neural networks with mixed random time-varying delays, Neurocomputing, 168, 896-907 (2015)
[31] Gahinet, P.; Nemirovskii, A.; Laub, A. J.; Chilali, M., LMI Control Toolbox for Use with MATLAB (1995), Natick, Mass, USA: The MathWorks, Natick, Mass, USA
[32] Du, Y.; Zhong, S.; Zhou, N.; Nie, L.; Wang, W., Exponential passivity of BAM neural networks with time-varying delays, Applied Mathematics and Computation, 221, 727-740 (2013) · Zbl 1329.93118
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