zbMATH — the first resource for mathematics

Finite-time stability analysis and stabilization for uncertain continuous-time system with time-varying delay. (English) Zbl 1307.93337
Summary: The problem of finite-time stability for a class of continuous-time system with norm-bounded uncertainties and time-varying delay is studied in this paper. The original system is firstly transformed into two interconnected subsystems. In order to extract the time-varying term of time delay, a two-term approximation of time-varying delay is used. By using the delay-dependent Lyapunov-Krasovskii-like functional and the method of linear matrix inequality (LMI), sufficient conditions for finite-time stability are derived. The derived conditions can analyze the finite-time stability of system and calculate the upper bound of time delay. In order to stabilize unstable system, the state-feedback and output-feedback controller are respectively designed. Results of numerical examples show the effectiveness of the proposed approach.

93D15 Stabilization of systems by feedback
93D30 Lyapunov and storage functions
93C15 Control/observation systems governed by ordinary differential equations
Full Text: DOI
[1] Lin, L.; Liu, X. D., Stability analysis for T-S fuzzy systems with interval time-varying delays and nonlinear perturbations, Int. J. Robust Nonlinear Control, 20, 14, 1622-1636, (2010) · Zbl 1204.93090
[2] Gu, Z.; Liu, J. L.; Peng, C.; Tian, E. G., Fault-distribution-dependent reliable fuzzy control for T-S fuzzy systems with interval time-varying delay, J. Chin. Inst. Eng., 35, 6, 633-640, (2012)
[3] Chen, Y. G.; Fei, S. M.; Zhang, K. J., Stabilisation for switched linear systems with time-varying delay and input saturation, Int. J. Syst. Sci., 45, 3, 532-546, (2014) · Zbl 1307.93302
[4] Wang, D.; Wang, W.; Shi, P., Exponential \(H_\infty\) filtering for switched linear systems with interval time-varying delay, Int. J. Robust Nonlinear Control, 19, 5, 532-551, (2009) · Zbl 1160.93328
[5] He, Y.; Zhang, Y.; Wu, M.; She, J. H., Improved exponential stability for stochastic Markovian jump systems with nonlinearity and time-varying delay, Int. J. Robust Nonlinear Control, 20, 1, 16-26, (2010) · Zbl 1192.93125
[6] Sathananthan, S.; Adetona, O.; Beane, C.; Keel, L. H., Feedback stabilization of Markov jump linear systems with time-varying delay, Stoch. Anal. Appl., 26, 3, 577-594, (2008) · Zbl 1147.93394
[7] Zhang, H.; Shi, Y.; Mehr, A. Saadat, Robust energy-to-peak filtering for networked systems with time-varying delays and randomly missing data, IET Control Theory Appl., 4, 12, 2921-2936, (2010)
[8] Zhang, H.; Shi, Y., Delay-dependent stabilization of discrete-time systems with time-varying delay via switching technique, J. Dyn. Syst. Meas. Control Trans. ASME, 134, 4, 044503, (2012)
[9] Wu, J.; Zhang, H.; Shi, Y., \(\operatorname{H}_2\) state estimation for network-based systems subject to probabilistic delays,”, Signal Process., 92, 11, 2700-2706, (2012)
[10] Ma, L.; Da, F. P., Exponential \(H_\infty\) filter design for stochastic time-varying delay systems with Markovian jumping parameters, Int. J. Robust Nonlinear Control, 20, 7, 802-817, (2010) · Zbl 1298.93330
[11] Chen, C.; Lee, C., Delay-independent stabilization of linear systems with time-varying delayed state and uncertainties, J. Frankl. Inst., 346, 4, 378-390, (2009) · Zbl 1166.93369
[12] Zhang, G. B.; Wang, T.; Li, T.; Fei, S. M., Delay-derivative-dependent stability criterion for neural networks with probabilistic time-varying delay, Int. J. Syst. Sci., 44, 11, 2140-2151, (2013) · Zbl 1307.93447
[13] Zuo, Z. Q.; Yang, C. L.; Wang, Y. J., A new method for stability analysis of recurrent neural networks with interval time-varying delay, IEEE Trans. Neural Netw., 21, 2, 339-344, (2010)
[14] Wu, L. G.; Su, X. J.; Shi, P.; Qiu, J. B., A new approach to stability analysis and stabilization of discrete-time T-S fuzzy time-varying delay systems, IEEE Trans. Syst. Man Cybern. B: Cybern., 41, 1, 273-286, (2011)
[15] Jiang, L.; Yao, W.; Wu, Q. H.; Wen, J. Y.; Cheng, S. J., Delay-dependent stability for load frequency control with constant and time-varying delays, IEEE Trans. Power Syst., 27, 2, 932-941, (2012)
[16] Wang, C.; Shen, Y., Delay partitioning approach to robust stability analysis for uncertain stochastic systems with interval time-varying delay, IET Control Theory Appl., 6, 7, 875-883, (2012)
[17] Li, X.; Gao, H. J., A new model transformation of discrete-time systems with time-varying delay and its application to stability analysis, IEEE Trans. Autom. Control, 56, 9, 2172-2178, (2011) · Zbl 1368.93102
[18] Zhang, B. Y.; Xu, S. Y.; Zou, Y., Improved stability criterion and its applications in delayed controller design for discrete-time systems, Automatica, 44, 11, 2963-2967, (2008) · Zbl 1152.93453
[19] Chen, G. P.; Yang, Y., Finite-time stability of switched positive linear systems, Int. J. Robust Nonlinear Control, 24, 1, 179-190, (2014) · Zbl 1278.93229
[20] Zhao, S. W.; Sun, J. T.; Liu, L., Finite-time stability of linear time-varying singular systems with impulsive effects, Int. J. Control, 81, 11, 1824-1829, (2008) · Zbl 1148.93345
[21] Yang, D. D.; Cai, Y. K., Finite-time reliable guaranteed cost fuzzy control for discrete-time nonlinear systems, Int. J. Syst. Sci., 42, 1, 121-128, (2011) · Zbl 1209.93088
[22] Xu, J.; Sun, J. T., Finite-time stability of nonlinear switched impulsive systems, Int. J. Syst. Sci., 44, 5, 889-895, (2013) · Zbl 1278.93231
[23] Kamenkov, G., On stability of motion over a finite interval of time, J. Appl. Math. Mech., 17, 529-540, (1953)
[24] P. Dorato, Short time stability in linear time-varying systems, in: Proceedings of the IRE International Convention Record Part, vol. 4, 1961, pp. 83-87.
[25] Shang, Y. L., Finite-time consensus for multi-agent systems with fixed topologies, Int. J. Syst. Sci., 43, 3, 499-506, (2012) · Zbl 1258.93014
[26] Zheng, Y. S.; Chen, W. S.; Wang, L., Finite-time consensus for stochastic multi-agent systems, Int. J. Control, 84, 10, 1644-1652, (2011) · Zbl 1236.93141
[27] Zheng, Y. S.; Wang, L., Finite-time consensus of heterogeneous multi-agent systems with and without velocity measurements, Syst. Control Lett., 61, 8, 871-878, (2012) · Zbl 1252.93009
[28] Su, Z.; Zhang, Q. L.; Ai, J.; Sun, X., Finite-time fuzzy stabilisation and control for nonlinear descriptor systems with non-zero initial state, Int. J. Syst. Sci., 46, 2, 364-376, (2015) · Zbl 1316.93070
[29] Amato, F.; Ariola, M.; Cosentino, C., Robust finite-time stabilisation of uncertain linear systems, Int. J. Control, 84, 12, 2117-2127, (2011) · Zbl 1236.93121
[30] Amato, F.; Ambrosino, R.; Ariola, M.; Tommasi, G. D., Robust finite-time stability of impulsive dynamical linear systems subject to norm-bounded uncertainties, Int. J. Robust Nonlinear Control, 21, 10, 1080-1092, (2011) · Zbl 1225.93087
[31] He, S. P.; Liu, F., Finite-time \(H_\infty\) fuzzy control of nonlinear jump systems with time delays via dynamic observer-based state feedback, IEEE Trans. Fuzzy Syst., 20, 4, 605-614, (2012)
[32] Moulay, E.; Dambrine, M.; Yeganefar, N.; Perruquetti, W., Finite-time stability and stabilization of time-delay systems, Syst. Control Lett., 57, 7, 561-566, (2008) · Zbl 1140.93447
[33] Zhang, Z.; Zhang, Z.; Zhang, H.; Zheng, B.; Karimi, H. R., Finite-time stability analysis and stabilization for linear discrete-time system with time-varying delay, J. Frankl. Inst., 351, 6, 3457-3476, (2014) · Zbl 1290.93147
[34] Liu, H.; Shen, Y.; Zhao, X. D., Finite-time stabilization and boundedness of switched linear system under state-dependent switching, J. Frankl. Inst., 350, 3, 541-555, (2013) · Zbl 1268.93078
[35] Shi, P.; Boukas, E. K.; Agarwal, R. K., Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay, IEEE Trans. Autom. Control, 44, 11, 2139-2144, (1999) · Zbl 1078.93575
[36] K. Gu, An integral inequality in the stability problem of time-delay systems, in: Proceedings of the 39th IEEE Conference on Decision and Control, 2000, pp. 2805-2810.
[37] Wang, D.; Wang, J. L.; Wang, W., \(H_\infty\) controller design of networked control systems with Markov packet dropouts, IEEE Trans. Syst. Man Cybern.: Syst., 43, 3, 689-697, (2013)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.