New results on stability analysis for systems with discrete distributed delay. (English) Zbl 1331.93166
Summary: The integral inequality technique is widely used to derive delay-dependent conditions, and various integral inequalities have been developed to reduce the conservatism of the conditions derived. In this study, a new integral inequality is devised that is tighter than existing ones. It is used to investigate the stability of linear systems with a discrete distributed delay, and a new stability condition is established. The results can be applied to systems with a delay belonging to an interval, which may be unstable when the delay is small or nonexistent. Three numerical examples demonstrate the effectiveness and the smaller conservatism of the method.
MSC:
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 93D30 | Lyapunov and storage functions |
References:
| [1] | Chen, W. H.; Zheng, W. X., Delay-dependent robust stabilization for uncertain neutral systems with distributed delays, Automatica, 43, 1, 95-104 (2007) · Zbl 1140.93466 |
| [2] | Fridman, E.; Shaked, U., An improved stabilization method for linear time-delay systems, IEEE Transactions on Automatic Control, 47, 11, 1931-1937 (2002) · Zbl 1364.93564 |
| [3] | Gu, K.; Kharitonov, V. L.; Chen, J., Stability of time-delay systems (2003), Birkhäuser: Birkhäuser Boston · Zbl 1039.34067 |
| [4] | Han, Q. L., Absolute stability of time-delay systems with sector-bounded nonlinearity, Automatica, 41, 12, 2171-2176 (2005) · Zbl 1100.93519 |
| [5] | Kao, C. Y.; Rantzer, A., Stability analysis of systems with uncertain time-varying delays, Automatica, 43, 6, 959-970 (2007) · Zbl 1282.93203 |
| [6] | Kim, J. H., Note on stability of linear systems with time-varying delay, Automatica, 47, 9, 2118-2121 (2011) · Zbl 1227.93089 |
| [7] | Park, P. G.; Ko, J. W., Stability and robust stability for systems with a time-varying delay, Automatica, 43, 10, 1855-1858 (2007) · Zbl 1120.93043 |
| [8] | Park, M. J.; Kwon, O. M.; Park, J. H.; Lee, S. M.; Cha, E. J., Stability of time-delay systems via Wirtinger-based double integral inequality, Automatica, 55, 5, 204-208 (2015) · Zbl 1377.93123 |
| [9] | Seuret, A.; Gouaisbaut, F., Wirtinger-based integral inequality: Application to time-delay systems, Automatica, 49, 9, 2860-2866 (2013) · Zbl 1364.93740 |
| [11] | Sun, J.; Liu, G. P.; Chen, J.; Rees, D., Improved delay-range-dependent stability criteria for linear systems with time-varying delays, Automatica, 46, 2, 466-470 (2010) · Zbl 1205.93139 |
| [12] | Wu, M.; He, Y.; She, J. H.; Liu, G. P., Delay-dependent criteria for robust stability of time-varying delay systems, Automatica, 40, 8, 1435-1439 (2004) · Zbl 1059.93108 |
| [13] | Zeng, H. B.; He, Y.; Wu, M.; She, J., Free-matrix-based integral inequality for stability analysis of systems with time-varying delay, IEEE Transactions on Automatic Control (2015) · Zbl 1360.34149 |
| [14] | Zhang, X. M.; Han, Q. L., New stability criterion using a matrix-based quadratic convex approach and some novel integral inequalities, IET Control Theory & Applications, 8, 12, 1054-1061 (2014) |
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