zbMATH — the first resource for mathematics

Stability analysis for continuous systems with two additive time-varying delay components. (English) Zbl 1120.93362
Syst. Control Lett. 56, No. 1, 16-24 (2007); corrigendum 56, No. 9-10, 662 (2007).
Summary: This paper presents a new result of stability analysis for continuous systems with two additive time-varying delay components, which represent a general class of delay systems with strong application background in network based control systems. This criterion is expressed as a set of linear matrix inequalities, which can be readily tested by using standard numerical software. A numerical example is provided to show the effectiveness and advantage of the proposed stability condition.
The Corrigendum gives the correct form of the matrix \(A\) in the illustrative example.

93D30 Lyapunov and storage functions
34K20 Stability theory of functional-differential equations
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
93C05 Linear systems in control theory
93A15 Large-scale systems
LMI toolbox
Full Text: DOI
[1] Cao, Y.-Y.; Sun, Y.-X.; Lam, J., Delay-dependent robust \(H_\infty\) control for uncertain systems with time-varying delays, IEE proc. part D: control theory appl., 145, 338-344, (1998)
[2] Fridman, E.; Shaked, U., Delay-dependent stability and \(H_\infty\) control: constant and time-varying delays, Internat. J. control, 76, 1, 48-60, (2003) · Zbl 1023.93032
[3] Gahinet, P.; Nemirovskii, A.; Laub, A.J.; Chilali, M., LMI control toolbox User’s guide, (1995), The Math. Works Inc. Natick, MA
[4] Gao, H.; Wang, C., Comments and further results on a descriptor system approach to \(H_\infty\) control of linear time-delay systems, IEEE trans. automat. control, 48, 3, 520-525, (2003) · Zbl 1364.93211
[5] Gu, K.; Kharitonov, V.L.; Chen, J., Stability of time-delay systems, (2003), Springer Berlin, Germany · Zbl 1039.34067
[6] Gu, K.; Niculescu, S.I., Survey on recent results in the stability and control of time-delay systems, J. dyn. syst. meas. control, 125, 158-165, (2003)
[7] Han, Q., Robust stability of uncertain delay-differential systems of neutral type, Automatica, 38, 719-723, (2002) · Zbl 1020.93016
[8] Jing, X.J.; Tan, D.L.; Wang, Y.C., An LMI approach to stability of systems with severe time-delay, IEEE trans. automat. control, 49, 7, 1192-1195, (2004) · Zbl 1365.93226
[9] Kolmanovskii, V.; Myshkis, A., Introduction to the theory and applications of functional differential equations, (1999), Kluwer Dordrecht, The Netherlands · Zbl 0917.34001
[10] Lee, Y.S.; Moon, Y.S.; Kwon, W.H.; Lee, K.H., Delay-dependent robust \(H_\infty\) control for uncertain systems with time-varying state-delay, (), 3208-3213
[11] Lee, Y.S.; Moon, Y.S.; Kwon, W.H.; Park, P.G., Delay-dependent robust \(H_\infty\) control for uncertain systems with a state-delay, Automatica, 40, 65-72, (2004) · Zbl 1046.93015
[12] Moon, Y.S.; Park, P.; Kwon, W.H.; Lee, Y.S., Delay-dependent robust stabilization of uncertain state-delayed systems, Internat. J. control, 74, 1447-1455, (2001) · Zbl 1023.93055
[13] Nian, X.; Feng, J., Guaranteed-cost control of a linear uncertain system with multiple time-varying delays: an LMI approach, IEE proc. part D: control theory appl., 150, 1, 17-22, (2003)
[14] Niculescu, S.I., Delay effects on stability: A robust control approach, (2001), Springer Heidelberg, Germany
[15] Park, P., A delay-dependent stability criterion for systems with uncertain time-invariant delays, IEEE trans. automat. control, 44, 4, 876-877, (1999) · Zbl 0957.34069
[16] Richard, J.P., Time-delay systems: an overview of some recent advances and open problems, Automatica, 39, 10, 1667-1694, (2003) · Zbl 1145.93302
[17] Wu, M.; He, Y.; She, J.H.; Liu, G.P., Delay-dependent criteria for robust stability of time-varying delay systems, Automatica, 40, 1435-1439, (2004) · Zbl 1059.93108
[18] Xu, B.; Liu, Y., Delay-dependent/delay-independent stability of linear systems with multiple time-varying delays, IEEE trans. automat. control, 48, 4, 697-701, (2003) · Zbl 1364.34108
[19] Yue, D.; Won, S., An improvement on delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty, IEEE trans. automat. control, 47, 407-408, (2002) · Zbl 1364.93609
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.