Stability and stabilizability of a class of uncertain dynamical systems with delays

• Autorzy: Mohammed Salah Saadni , Driss Mehdi
• Języki publikacji: EN

Abstrakty

EN

This paper deals with a class of uncertain systems with time-varying delays and norm-bounded uncertainty. The stability and stabilizability of this class of systems are considered. Linear Matrix Inequalities (LMI) delay-dependent sufficient conditions for both stability and stabilizability and their robustness are established.

Słowa kluczowe

EN

dynamical systems; time-varying delays; robust stabilizability; norm-bounded robust stability; time-varying uncertainty

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2005
• Tom: 15
• Numer: 3
• Strony: 321-329

Daty

wydano

2005

otrzymano

2004-05-23

poprawiono

2005-01-22

Twórcy

autor

Mohammed Salah Saadni

• L.A.I.I, ESIP, 40 Avenue du Recteur Pineau, 86022 Poitiers Cedex, France

autor

Driss Mehdi

• Automatic Control Research Unit, Electrical Engineering Department, Sfax National Engineering School, B.P. 805 Route Menzel Chaker Km 0.5, 3038 Sfax, Tunisia

Bibliografia

• Boukas E.-K. and Liu Z.-K. (2002): Deterministic and Stochastic Time-Delay Systems. -Boston: Birkhauser, Marcel Dekker.
• de la Sen M. (2002): Stability test for two common classes of linear time-delay systems and hybrid systems. - Lutianian Math. J., Vol. 42, No. 2, pp. 153-168.
• Hale J.-K. (1977): Theory of Functional Differential Equations. -New York: Springer.
• Hmamed A. (1997): Further results on the robust stability of uncertain linear systems including delayed perturbations. -Automatica, Vol. 33, No. 9, pp. 1763-1765.
• Kim J.-H. (2001): Delay and its time derivative dependent robust stability of time-delayed linear systems with uncertainty. -IEEETAC, Vol. 46, No. 5, pp. 789-792.
• Lee B. and Lee J.-G. (1999): Robust stability and stabilization of linear delayed systems with structured uncertainty. -Automatica, Vol. 35, No. 6, pp. 1149-1154.
• Lee B. and Lee J.-G. (2000): Robust control of uncertain systems with input delay and input sector nonlinearity. -Proc. 39th IEEE Conf. Decision and Control, North Sydney, Australia, Vol. 5, pp. 4430-4435.
• Li X. and de Souza C.-E. (1996): Criteria for robust stability of uncertain linear systems with time-varying state delays. -Proc. 13th IFAC World Congress, San Francisco, CA, pp. 137-142.
• Li X. and de Souza C.-E. (1997a): Criteria for robust stability of uncertain linear systems with state delays. - Automatica, Vol. 33, No. 9, pp. 1657-1662.
• Li X. and de Souza C.-E. (1997b): Delay dependent robust stability and stabilization of uncertain linear delay systems: A linear matrix inequality approach. - IEEETAC, Vol. 42, No. 8, pp. 1144-1148.
• Li X., Fu M., and de Souza C.-E. (1992): H_∞ control and quadratic stabilization of systems with parameter uncertainty via output feedback. - IEEETAC, Vol. 37, No. 8, pp. 1253-1256.
• Mahmoud M.-S. (2000): Robust Control and Filtering for Time-Delay Systems. - New York: Marcel-Dekker.
• Marchenko V.-M., Borkovskaja I.-M. and Jakimenko A.-A. (1996): Linear state-feedback for after-effect systems: stabilization and modal control. - Proc. 13th IFAC World Congress, San-Francisco, USA, pp. 441-446.
• Niculescu S.-I., de Souza C.-E., Dion J.-M. and Dugard L. (1994): Robust stability and stabilization of uncertain linear systems with state delay: Single dealy case. - Proc. IFAC Symp. Robust Control Design, Rio de Janero, Brazil, pp. 469-474.
• Su J.-H. (1994): Further results on the robust stability of linear systems with a single time-delay. - SCL, Vol. 23, pp. 375-379.
• Su T.J. and Huang C.-G. (1992): Robust stability of delay dependence for linear systems. -IEEETAC, Vol. 37, No. 10, pp. 1656-1659.
• Sun Y.J., Hsieh J.-G. and Yang H.-C. (1997): On the stability of uncertain systems with multiple time-varying delays. - IEEETAC, Vol. 42, No. 1, pp. 101-105.
• Wang S.-S., Chen B.-S. and Lin T.-P. (1987): Robust stability of uncertain time-delay systems. -IJC, Vol. 46, No. 4, pp. 963-976.
• Xu B. (1995): On delay-independent stability of large scale systems with time-delays. - IEEETAC, Vol. 40, No. 5, pp. 930-933.
• Xu B. and Liu Y. (1994): An improved Razimukhin-type theorem and its applications.- IEEETAC, Vol. 39, No. 4, pp. 839-841.