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.
MSC:
| 93D15 | Stabilization of systems by feedback |
| 93D30 | Lyapunov and storage functions |
| 93C15 | Control/observation systems governed by ordinary differential equations |
Keywords:
finite-time stability; continuous-time system; norm-bounded uncertainties; time-varying delay; delay-dependent Lyapunov-Krasovskii-like functional; linear matrix inequality (LMI); state-feedback and output-feedback controllerReferences:
| [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., \(H_2\) 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) · Zbl 0055.32101 |
| [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 |
| [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) |
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