New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems. (English) Zbl 0974.93028

Summary: A new (descriptor) model transformation and a corresponding Lyapunov-Krasovskii functional are introduced for stability analysis of systems with delays. Delay-dependent/delay-independent stability criteria are derived for linear retarded and neutral type systems with discrete and distributed delays. Conditions are given in terms of linear matrix inequalities and for the first time refer to neutral systems with discrete and distributed delays. The proposed criteria are less conservative than other existing criteria (for retarded type systems and neutral systems with discrete delays) since they are based on an equivalent model transformation and since they require bounds for fewer terms. Examples are given that illustrate advantages of our approach.


93C23 Control/observation systems governed by functional-differential equations
93D20 Asymptotic stability in control theory
93B17 Transformations
15A39 Linear inequalities of matrices
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[1] Charitonov, V.; Melchor-Aguilar, D., On delay-dependent stability conditions, Systems Control Lett., 40, 71-76 (2000) · Zbl 0977.93072
[4] Hale, J.; Lunel, S., Introduction to Functional Differential Equations (1993), Springer: Springer New York · Zbl 0787.34002
[5] Hale, J.; Lunel, S., Effects of small delays on stability and control, Rapportnr. WS-528 (1999), Vrije University: Vrije University Amsterdam
[6] Kolmanovskii, V.; Niculescu, S.-I.; Richard, J. P., On the Liapunov-Krasovskii functionals for stability analysis of linear delay systems, Internat. J. Control, 72, 374-384 (1999) · Zbl 0952.34057
[7] Kolmanovskii, V.; Richard, J-P., Stability of some linear systems with delays, IEEE Trans. Automat. Control, 44, 984-989 (1999) · Zbl 0964.34065
[8] Li, X.; de Souza, C., Criteria for robust stability and stabilization of uncertain linear systems with state delay, Automatica, 33, 1657-1662 (1997) · Zbl 1422.93151
[9] 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
[10] Logemann, H.; Townley, S., The effect of small delays in the feedback loop on the stability of the neutral systems, Systems Control Lett., 27, 267-274 (1996) · Zbl 0866.93089
[11] Mahmoud, M., Robust Control and Filtering for Time-Delay Systems (2000), Marcel Dekker: Marcel Dekker New York
[13] Niculescu, S.-I., Further remarks on delay-dependent stability of linear neutral systems, Proc. of MTNS 2000 (2000), Perpignan: Perpignan France
[14] Takaba, K.; Morihira, N.; Katayama, T., A generalized Lyapunov theorem for descriptor system, Systems Control Lett., 24, 49-51 (1995) · Zbl 0883.93035
[15] Verriest, E.; Niculescu, S.-I., Delay-independent stability of linear neutral systems: a Riccati equation approach, (Dugard, L.; Verriest, E., Stability and Control of Time-Delay Systems. Stability and Control of Time-Delay Systems, Lecture Notes in Control and Information Sciences, Vol. 227 (1997), Springer: Springer London), 92-100 · Zbl 0923.93049
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