Title:
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New criterion for asymptotic stability of time-varying dynamical systems (English) |
Author:
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Ghrissi, Taoufik |
Author:
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Hammami, Mohamed Ali |
Author:
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Hammi, Mekki |
Author:
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Mabrouk, Mohamed |
Language:
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English |
Journal:
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Kybernetika |
ISSN:
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0023-5954 (print) |
ISSN:
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1805-949X (online) |
Volume:
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53 |
Issue:
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2 |
Year:
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2017 |
Pages:
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331-353 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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In this paper, we establish some new sufficient conditions for uniform global asymptotic stability for certain classes of nonlinear systems. Lyapunov approach is applied to study exponential stability and stabilization of time-varying systems. Sufficient conditions are obtained based on new nonlinear differential inequalities. Moreover, some examples are treated and an application to control systems is given. (English) |
Keyword:
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nonlinear time-varying systems |
Keyword:
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asymptotic stability |
Keyword:
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stabilization |
MSC:
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93Cxx |
MSC:
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93Dxx |
idZBL:
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Zbl 06770171 |
idMR:
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MR3661355 |
DOI:
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10.14736/kyb-2017-2-0331 |
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Date available:
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2017-06-25T18:02:32Z |
Last updated:
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2018-01-10 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/146808 |
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Reference:
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[1] Aeyels, O., Penteman, P.: A new asymptotic stability cretirion for non linear time varying differential equations..IEEE Trans. Automat. Control 43 (1998), 968-971. MR 1633504, 10.1109/9.701102 |
Reference:
|
[2] Bay, N. S., Phat, V. N.: Stability of nonlinear difference time varying systems with delays..Vietnam J. Math. 4 (1999), 129-136. |
Reference:
|
[3] BenAbdallah, A., Ellouze, I., Hammami, M. A.: Practical stability of nonlinear time-varying cascade systems..J. Dynamical Control Systems 15 (2009), 1, 45-62. Zbl 1203.93160, MR 2475660, 10.1007/s10883-008-9057-5 |
Reference:
|
[4] Corless, M: Guaranteed rates of exponential convergence for uncertain systems..J. Optim. Theory Appl. 64 (1990), 3, 481-494. MR 1043736, 10.1007/bf00939420 |
Reference:
|
[5] Corless, M., Leitmann, G.: Controller design for uncertain systems via Lyapunov functions..In: Proc. 1988 American Control Conference, Atlanta 1988. |
Reference:
|
[6] Garofalo, F., Leitmann, G.: Guaranteeing ultimate boundedness and exponential rate of convergence for a class of nominally linear uncertain systems..J. Dynamic Systems, Measurement, and Control 111 (1989), 584-588. Zbl 0714.93013, 10.1115/1.3153097 |
Reference:
|
[7] Hahn, W.: Stability of Motion..Springer, New York 1967. Zbl 0189.38503, MR 0223668, 10.1007/978-3-642-50085-5 |
Reference:
|
[8] A.Hammami, M.: On the stability of nonlinear control systems with uncertainty..J. Dynamical Control Systems 7 (2001), 2, 171-179. MR 1830490, 10.1023/a:1013099004015 |
Reference:
|
[9] Hammi, M., Hammami, M. A.: Non-linear integral inequalities and applications to asymptotic stability..IMA J. Math. Control Inform. 32 (2015), 4, 717-736. Zbl 1328.93214, MR 3436122, 10.1093/imamci/dnu016 |
Reference:
|
[10] Hammi, M., A.Hammami, M.: Gronwall-Bellman type integral inequalities and applications to global uniform asymptotic stability..CUBO Math. J. 17 (2015), 3, 53-70. MR 3445845, 10.4067/s0719-06462015000300004 |
Reference:
|
[11] Khalil, H.: Nonlinear Systems..Prentice Hall 2002. Zbl 1194.93083 |
Reference:
|
[12] Lakshmikantham, V., Leela, S., Martynuk, A. A.: Practical Stability of Nonlinear Systems..World Scientific Publishing Co. Pte. Ltd. 1990. MR 1089428, 10.1142/1192 |
Reference:
|
[13] Lü, J., Chen, G.: A time-varying complex dynamical network model and its controlled synchronization criteria..IEEE Trans. Automat. Control. 50 (2005), 6, 841-846. MR 2142000, 10.1109/tac.2005.849233 |
Reference:
|
[14] Liu, K., Zhu, H., Lü, J.: Bridging the gap between transmission noise and sampled data for robust consensus of multi-agent systems..IEEE Trans. Circuits and Systems I 62 (2015), 7, 1836-1844. MR 3361623, 10.1109/tcsi.2015.2434101 |
Reference:
|
[15] Liu, K., Wu, L., Lü, J., Zhu, H.: Finite-time adaptive consensus of a class of multi-agent systems..Science China Technol. Sci. 59 (2016), 1, 22-32. 10.1007/s11431-015-5989-7 |
Reference:
|
[16] Li, Y., Wu, X., Lu, J., Lü, J.: Synchronizability of duplex networks..IEEE Trans. Circuits and Systems II - Express Briefs 63 (2016), 2, 206-210. 10.1109/tcsii.2015.2468924 |
Reference:
|
[17] Lin, W., Pongvuthithum, R.: Global satbilization of cascade system by ${C}^0$ partial-state feedback..IEEE Trans. Automat. Control 47 (2002), 1356-1362. MR 1917450, 10.1109/tac.2002.800743 |
Reference:
|
[18] Pantely, E., Loria, A.: On global uniform asymptotic stability of nonlinear time-varying systems in cascade..System Control Lett. 33 (1998), 131-138. MR 1607815, 10.1016/s0167-6911(97)00119-9 |
Reference:
|
[19] Pham, Q. C., Tabareau, N., Slotine, J. J. E.: A contraction theory appoach to stochastic incremental stability..IEEE Trans. Automat. Control 54 (2009), 4, 816-820. MR 2514815, 10.1109/tac.2008.2009619 |
Reference:
|
[20] Phat, V. N.: Global stabilization for linear continuous time-varying systems..Appl. Math. Comput. 175 (2006), 1730-1743. Zbl 1131.93044, MR 2225620, 10.1016/j.amc.2005.09.017 |
Reference:
|
[21] Martynyuk, A. A.: Stability in the models of real world phenomena..Nonlinear Dyn. Syst. Theory 11 (2011), 1, 7-52. Zbl 1283.70006, MR 2798814 |
Reference:
|
[22] Mu, X., Cheng, D.: On stability and stabilization of time-varying nonlinear control systems..Asian J. Control 7 (2005), 3, 244-255. 10.1111/j.1934-6093.2005.tb00234.x |
Reference:
|
[23] Pata, V.: Uniform estimates of Gronwall types..J. Math. Anal. Appl. xx (2011), 264-270. MR 2684477, 10.1016/j.jmaa.2010.07.006 |
Reference:
|
[24] Zubov, V. I.: Methods of A. M. Lyapunov and Their Applications..P. Noordhoff, Groningen, 1964. MR 0179428 |
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