Robust H∞ performance for linear delay-differential systems with time-varying uncertainties

IEEE Transactions on Automatic Control

Volumn 43, Issue 2, 1998, Pages 223-226

  Kokame, H ^a   Kobayashi, H ^b   Mori, T ^c  

^a Osaka Prefecture University   (Japan)

^b OSAKA INSTITUTE OF TECHNOLOGY   (Japan)

^c KYOTO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Linear matrix inequality; Robust H performance; Time delay; Time varying uncertainties

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; DELAY CONTROL SYSTEMS; DIFFERENTIAL EQUATIONS; LYAPUNOV METHODS; MATRIX ALGEBRA; OPTIMAL CONTROL SYSTEMS; PERTURBATION TECHNIQUES; ROBUSTNESS (CONTROL SYSTEMS); STABILITY CRITERIA; TIME VARYING SYSTEMS;

LINEAR DELAY DIFFERENTIAL SYSTEMS; LINEAR MATRIX INEQUALITY; PARAMETER UNCERTAINTIES;

LINEAR CONTROL SYSTEMS;

EID: 0031997087     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.661069     Document Type: Article

References (18)

1. ∞ control for linear systems with norm-bounded time-varying uncertainty," IEEE Trans. Automat. Contr., vol. 37, pp. 1188-1191, 1992.
2. ∞ control and quadratic stabilization of systems with parameter uncertainty via output feedback," IEEE Trans. Automat. Contr., vol. 37, pp. 1253-1256, 1992.
3. ∞ control of systems under norm bounded uncertainties in all system matrices," IEEE Trans. Automat. Contr., vol. 39, pp. 1320-1322, 1994.
4. J. C. Shen, B. S. Chen, and F. C. Kung, "Memoryless stabilization of uncertain dynamic delay systems: Riccati equation approach," IEEE Trans. Automat. Contr., vol. 36, pp. 638-640, 1991.
5. S. Phoojaruenchanachai and K. Furuta, "Memoryless stabilization of uncertain linear systems including time-varying state delays," IEEE Trans. Automat. Contr., vol. 37, pp. 1022-1026, 1992.
6. M. S. Mahmoud and N. F. Al-Muthairi, "Design of robust controllers for time-delay systems," IEEE Trans. Automat. Contr., vol. 39, pp. 995-999, 1994.
7. ∞ controllers for state delayed systems," IEEE Trans. Automat. Contr., vol. 39, pp. 159-162, 1994.
8. A. Kojima, K. Uchida, E. Shimemura, and S. Ishijima, "Robust stabilization of a system with delays in control," IEEE Trans. Automat. Contr., vol. 39, pp. 1694-1698, 1994.
9. J. Hale: Theory of Functional Differential Equations. New York: Springer-Verlag, 1977.
10. B. R. Barmish, "Necessary and sufficient conditions for quadratic stabilizability of an uncertain system," J. Optimiz. Theory Appl., vol. 46, pp. 399-408, 1985.
11. I. R. Petersen and C. V. Hollot, "A Riccati equation approach to the stabilization of uncertain linear systems," Automatica, vol. 22, pp. 397-411, 1986.
12. J. Louisell, "Growth estimates and asymptotic stability for a class of differential-delay equation having time-varying delay," J. Math. Analysis Appl., vol. 164, pp. 453-479, 1992.
13. E. W. Kamen, "On the relationship between zero criteria for two-variable polynomials and asymptotic stability of delay differential equations," IEEE Trans. Automat. Contr., vol. AC-25, pp. 983-984, 1980.
14. R. M. Lewis and B. D. O. Anderson, "Necessary and sufficient conditions for delay-independent stability of linear autonomous systems," IEEE Trans. Automat. Contr., vol. AC-25, pp. 735-739, 1980.
15. S. D. Brierley, J. N. Chiasson, E. B. Lee, and S. H. Zak, "On stability independent of delay for linear systems," IEEE Trans. Automat. Contr., vol. AC-27, pp. 252-254, 1982.
16. E. W. Kamen, "Correction to 'Linear systems with commensurate time delays: Stability and stabilization independent of delay,'" IEEE Trans. Automat. Contr., vol. AC-28, pp. 248-249, 1983.
17. J. Louisell, "Absolute stability in linear delay-differential systems: III-posedness and robustness," IEEE Trans. Automat. Contr., vol. 40, pp. 1288-1291, 1995.
18. S. Boyd, L. EL Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.