Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-12-03T00:02:33.175Z Has data issue: false hasContentIssue false
  • English
  • Français

Observer-based robust H∞, control for uncertain time-delay systems

Published online by Cambridge University Press:  17 February 2009

Xinping Guan ,
Yichang Liu ,
Cailian Chen  and
Peng Shi
Xinping Guan
Affiliation:
Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004, P. R. China; e-mail: [email protected].
Yichang Liu
Affiliation:
Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004, P. R. China; e-mail: [email protected].
Cailian Chen
Affiliation:
Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004, P. R. China; e-mail: [email protected].
Peng Shi
Affiliation:
All correspondence should be addressed to this author. He was at the University of South Australia; he is now with Weapons Systems Division, Defence Science and Technology Organisation, PO Box 15OO, Edinburgh 5111 SA, Australia; e-mail: [email protected].
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we present a method for the construction of a robust observer-based H∞ controller for an uncertain time-delay system. Cases of both single and multiple delays are considered. The parameter uncertainties are time-varying and norm-bounded. Observer and controller are designed to be such that the uncertain system is stable and a disturbance attenuation is guaranteed, regardless of the uncertainties. It has been shown that the above problem can be solved in terms of two linear matrix inequalities (LMIs). Finally, an illustrative example is given to show the effectiveness of the proposed techniques.

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 4 , April 2003 , pp. 625 - 634
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Boyd, S., El Ghaoui, L., Feron, E. and Balakrishnan, V., Linear matrix inequalities in systems and control theory, Studies in Appl. Math. 15 (SIAM, Philadelphia, 1994).CrossRefGoogle Scholar
[2]Chen, J. C., “Designing stabilizing controllers and observers for uncertain linear systems with time-varying delay”, IEE Proc.-Control Theory Appl. 144 (1997) 331–333.Google Scholar
[3]Fattouh, A., Sename, O. and Dion, J. H., “Robust observer design for time-delay systems: A Riccati equation approach”, Kybernetika (Prague) 35 (1999) 753–764.Google Scholar
[4]Ge, J. H., Frank, P. M. and Lin, C. F., “Robust state feedback control for linear systems with state delay and parameter uncertainty”, Automatica J. IFAC 32 (1996) 1183–1185.CrossRefGoogle Scholar
[5]Jeung, E. T., Kim, J. H. and Park, H. B., “Output feedback controller design for linear systems with time-varying delayed state”, IEEE Trans. Automat. Control 43 (1998) 971–973.CrossRefGoogle Scholar
[6]Kokame, H., Kobayashi, H. and Mori, T., “Robust performance for linear delay-differential systems with time-varying uncertainties”, IEEE Trans. Automat. Control 43 (1998) 223–226.CrossRefGoogle Scholar
[7]Kreindler, E. and Jameson, A., “Conditions for nonnegativeness of partitioned matrices”, IEEE Trans. Automat. Control 17 (1972) 147–148.CrossRefGoogle Scholar
[8]Li, X. and Souza, C. E. D., “Criteria for robust stability and stabilization of uncertain linear systems with state delay”, Automatica J. IFAC 33 (1997) 1657–1662.CrossRefGoogle Scholar
[9]Shaked, U., Yaesh, I. and de Souza, C. E., “Bounded real criteria for linear time systems with state-delay and norm-bounded time-varying uncertainties”, IEEE Trans. Automat. Control 43 (1998) 1016–1021.CrossRefGoogle Scholar
[10]Shi, P., “Filtering on sampled-data systems with parametric uncertainty”, IEEE Trans. Automat. Control 43 (1998) 1022–1027.Google Scholar
[11]Shi, P., Boukas, E. K. and Agarwal, R. K., “Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay”, IEEE Trans. Automat. Control 44 (1999) 2139–2144.Google Scholar
[12]Trinh, H. and Aldeen, M., “Robust stability of singularly perturbed discrete-delay systems”, IEEE Trans. Automat. Control 40 (1995) 1620–1623.CrossRefGoogle Scholar
[13]Wang, H. S. and Yung, C. F., “Bounded real lemma and H ∞ control for descriptor systems”, IEEE Proc.-Control Theory Appl. 145 (1998) 316–322.CrossRefGoogle Scholar
[14]Wu, H. S., “Eigenstructure assignment-based robust stability conditions for uncertain systems with multiple time-varying delays”, Automatica J. IFAC 33 (1997) 97–102.CrossRefGoogle Scholar
[15]Xu, B. G., “Stability robustness bounds for linear systems with multiple time-varying delayed perturbations”, Internal. J. Systems Sci. 28 (1997) 1311–1317.CrossRefGoogle Scholar
[16]Yang, H. and Saif, M., “Observer design and fault diagnosis for state-retarded dynamical systems”, Automatica J. IFAC 34 (1998) 217–227.CrossRefGoogle Scholar
[17]Yang, S. K. and Chen, C. L., “Observer-based robust controller design for a linear systems with time-varying perturbations”, J. Math. Anal. Appl. 213 (1997) 642–661.CrossRefGoogle Scholar