Browse > Article

Delay-Dependent Stabilization for Uncertain Dynamic Systems with State and Input Delays  

Cho Hyun-Ju (영남대학교 전기공학과)
Park Ju-Hyun (영남대학교 전기공학과)
Publication Information
The Transactions of the Korean Institute of Electrical Engineers D / v.54, no.4, 2005 , pp. 215-219 More about this Journal
Abstract
This paper aims at asymptotic stabilization for uncertain dynamic systems with state and input delays. We propose a memoryless state feedback controller which maximizes the delay bound for guaranteeing stability of the system. Using Lyapunov method and linear matrix inequality (LMI) approach, a delay-dependent stabilization criterion is devised by taking the relationship between the terms in the Leibniz-Newton formula into account. The criterion is represented in terms of LMIs, which can be solved by various efficient convex optimization algorithms. Numerical examples are given to illustrate our main method.
Keywords
Citations & Related Records
연도 인용수 순위
  • Reference
1 Esfahani S. H. Petersen I. R. An LMI approach to output-feedback-guaranteed cost control for uncertain time-delay systems, International Journal of Robust and Nonlinear Control, vol. 10, pp. 157-174, 2000   DOI   ScienceOn
2 L. Yu, J. Chu, An LMI approach to guaranteed cost control of linear uncertain time-delay systems, Automatica, vol. 35, pp. 1155-1159, 1999   DOI   ScienceOn
3 P. -L. Liu and I.-J. Su, 'Stability for single and large-scale uncertain systems with time-varying delays', IEE Proceeding Control Theory Application, Vol. 146, pp. 591-597, 1999   DOI   ScienceOn
4 S. S. L. Chang, T. K. C. Peng, Adaptive guaranteed cost control of systems with uncertain parameters, IEEE translation on Automatic Control, AC-17 pp. 474-483, 1972   DOI
5 I. R. Petersen, Optimal guaranteed cost control and filtering for uncertain linear systems, IEEE translation on Automatic Control, AC-37 pp. 1971-1977, 1994   DOI   ScienceOn
6 M. Zribi and M. S. Mahmoud, '$H_{\infty}$-control design for systems with multiple delay', Computers and Electrical Engineering, Vol. 25, pp. 451-475, 1999   DOI   ScienceOn
7 E. Fridman and U. Shaked, 'An improved stabilization method for linear time-delay systems', IEEE Translations on Automatic Control, Vol. 47, pp. 1931-1937, 2002   DOI   ScienceOn
8 V. Kapila and W. M. Haddad, 'Memoryless $H_{\infty}$ controllers for discrete time systems with time delay', Automatica, Vol. 35, pp.1443-1451, 1998   DOI   ScienceOn
9 S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, linear Matrix Inequalities in Systems and Control Theory, Philadelphia, PA:SIAM, 1994
10 X. Li and C. de Souza, 'Delay-dependent robust stability and stabilization of uncertain linear delay systems: A linear matrix inequality approach', IEEE Translations on Automatic control. Vol. 42, pp. 1144-1148, 1997   DOI   ScienceOn
11 L. Xie, 'Output feedback $H_{\infty}$ control of systems with parameter uncertainty', International Journal of Control, Vol. 63, pp.1656-1659, 1996
12 X. Li and C. de Souza, 'Criteria for robust stability and stabilization of uncertain linear systems with state delay,' Automatica, Vol. 22, pp. 1657-1662, 1997   DOI   ScienceOn
13 P. Park, 'A delay-dependent stability criterion for systems with uncertain time-invariant delays,' IEEE Translations on Automatic Control, Vol. 44. pp. 876-877, April 1999   DOI   ScienceOn
14 Y. S. Moon, P. Park, W. H. Kwon, and Y. S. Lee, 'Delay-dependent robust stabilization of uncertain state-delayed systems', International Journal of Control, Vol. 74, pp. 1447-1455, 2001   DOI   ScienceOn
15 M. Wu, Y. He, J. -H She, and G. -P Liu, 'Delay-dependent criteria for robust stability of time-varying delay systems', Automatica, Vol. 40, pp. 1435-1439, 2004   DOI   ScienceOn
16 D. Yue, 'Robust stabilization of uncertain systems with unknown input delay', Automatica, Vol. 40. pp. 331-336, 2004   DOI   ScienceOn
17 J. Hale and S.M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993