Delay-dependent stability criterion for neutral time-delay systems via linear matrix inequality approach. (English) Zbl 1010.93084
The authors consider the following system
\[
\dot{x}(t)=Ax(t)+Bx(t-h)+C\int_{t-\tau}^{t} x(s) ds+D\dot{x}(t-\eta),\quad t\geq 0.
\]
A condition of asymptotic stability in the form of a delay-dependent linear matrix inequality is obtained. Some numerical examples are given.
Reviewer: Tamaz Tadumadze (Tbilisi)
MSC:
| 93D20 | Asymptotic stability in control theory |
| 34K40 | Neutral functional-differential equations |
| 15A39 | Linear inequalities of matrices |
| 93C23 | Control/observation systems governed by functional-differential equations |
References:
| [1] | Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory (1994), SIAM: SIAM Philadelphia · Zbl 0816.93004 |
| [2] | Dugard, L.; Verriest, E. I., Stability and Control of Time-Delay Systems (1997), Springer-Verlag: Springer-Verlag London |
| [3] | Hale, J. K.; Verduyn Lunel, S. M., Introduction to Functional Differential Equations (1993), Springer-Verlag: Springer-Verlag New York · Zbl 0787.34002 |
| [4] | Huang, Y. P.; Zhou, K., Robust stability of uncertain time-delay systems, IEEE Trans. Automat. Control, 45, 2169-2173 (2000) · Zbl 0989.93066 |
| [5] | Hui, G. D.; Hu, G. D., Simple criteria for stability of neutral systems with multiple delays, Internat. J. Systems Sci., 28, 1325-1328 (1997) · Zbl 0899.93031 |
| [6] | Ivanescu, D.; Dion, J. M.; Dugard, L.; Niculescu, S. I., Dynamical compensation for time-delay systems: an LMI approach, Internat. J. Robust Nonlinear Control, 10, 611-628 (2000) · Zbl 0963.93073 |
| [7] | Kim, J. H., Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty, IEEE Trans. Automat. Control, 46, 789-792 (2001) · Zbl 1008.93056 |
| [8] | Kolmanovskii, V. B., Stability of Functional Differential Equations (1986), Academic Press: Academic Press London · Zbl 0840.34084 |
| [9] | Kolmanovskii, V. B.; Myshkis, A., Introduction to the Theory and Applications of Functional Differential Equations (1999), Kluwer: Kluwer Dordrecht · Zbl 0917.34001 |
| [10] | Kolmanovskii, V. B.; Richard, J. P., Stability of some linear systems with delays, IEEE Trans. Automat. Control, 44, 984-989 (1999) · Zbl 0964.34065 |
| [11] | Lien, C. H.; Yu, K. W.; Hsieh, J. G., Stability conditions for a class of neutral systems with multiple time delays, J. Math. Anal. Appl., 245, 20-27 (2000) · Zbl 0973.34066 |
| [12] | Liu, P. L.; Su, T. J., Robust stability of interval time-delay systems with delay-dependence, Systems Control Lett., 33, 231-239 (1998) · Zbl 0902.93052 |
| [13] | Logemann, H.; Rebarber, R., The effect of small time-delays on the closed-loop stability of boundary control systems, Math. Control Signals Systems, 9, 123-151 (1996) · Zbl 0874.93077 |
| [14] | Logemann, H.; Rebarber, R.; Weiss, G., Conditions for robustness and nonrobustness of the stability of feedback systems with respect to small delays in the feedback loop, SIAM J. Control Optim., 34, 572-600 (1996) · Zbl 0853.93081 |
| [15] | Longemann, H.; Townley, S., The effect of small delays in the feedback loop on the stability of neutral systems, System Control Lett., 27, 267-274 (1996) · Zbl 0866.93089 |
| [16] | Mahmoud, M. S., Robust \(H∞\) control of linear neutral systems, Automatica, 36, 757-764 (2000) · Zbl 0988.93024 |
| [17] | Niculescu, S. I., On delay dependent stability under model transformations of some neutral linear systems, Internat. J. Control, 74, 609-617 (2001) · Zbl 1047.34088 |
| [18] | Park, J. H.; Won, S., Stability analysis for neutral delay-differential systems, J. Franklin Inst., 337, 1-9 (2000) · Zbl 0992.34057 |
| [19] | Spong, M. W., A theorem on neutral delay systems, Systems Control Lett., 6, 291-294 (1985) · Zbl 0573.93048 |
| [20] | Verriest, E. I.; Niculescu, S. I., Delay-independent stability of linear neutral systems: a Riccati equation approach, (Proceedings of European Control Conference, Brussels (1997)) · Zbl 0923.93049 |
| [21] | Yan, J. J., Robust stability analysis of uncertain time delay systems with delay-dependence, Electron. Lett., 37, 135-137 (2001) |
| [22] | Zhang, J.; Knopse, C. R.; Tsiotras, P., Stability of time-delay systems: equivalence between Lyapunov and scaled small-gain conditions, IEEE Trans. Automat. Control, 46, 482-486 (2001) · Zbl 1056.93598 |
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