Robust Stability Condition for a Class of Time-Delay Plants with Uncertainty

Main Article Content

Kou Yamada
Takaaki Hagiwara
Hideharu Yamamoto

Abstract

In this paper, we consider the robust stability condition for single-input/single-output time-delay plants with new class of uncertainties. First of all, we de¯ne a class of uncertainties to be considered. The necessary and sufficient robust stability condition for time-delay plants with such class of uncertainties is presented. The relation between the time-delay plant and the nominal time-delay plant to satisfy the robust stability condition is clarified. By using this relation, we will show the necessary and sufficient robust stability condition for the time-delay plant with varying number of right half plane poles.

Article Details

How to Cite
Yamada, K., Hagiwara, T., & Yamamoto, H. (2008). Robust Stability Condition for a Class of Time-Delay Plants with Uncertainty. ECTI Transactions on Electrical Engineering, Electronics, and Communications, 7(1), 34–41. https://doi.org/10.37936/ecti-eec.200971.171805
Section
Research Article

References

[1] J.C. Doyle and G. Stein, "Multivariable feedback design: concepts for a classical modern synthesis" IEEE Trans. on Automatic Cotrol, Vol.AC-26, pp.4-16, 1981

[2] J.C. Doyle, J.E. Wall and G. Stein, "Performance and robustness analysis for structured uncertainty" Proc. 21st IEEE conf. CDC, pp.629-636, 1982

[3] M.J. Chen and C.A. Desoer, " Necessary and Sufficient condition for robust stability of linear distributed feedback systems" International Journal of Control, Vol.35, pp.255-267, 1982

[4] M.S. Verma, J.W. Helton and E.A.Jonckheere, " Robust stabilization of a family of plants with varying number of right half plane poles" Proceedings of 1986 American Control Conference, pp.1827-1832, 1986

[5] K. Glover and J.C.Doyle, " State-space formulae for all stabilizing controllers that satisfy an H1 norm bound and relations to risk sensitivity" Systems & Control Letters, Vol.11, pp.167-172, 1988

[6] J.C. Doyle, K. Glover, P.P. Khargonekar and B.A. Francis, " State-space solution to standard H2 and H1 control problems" IEEE Trans. on Automatic Control, Vol.AC-34, pp.831-847, 1989

[7] H. Kimura, "Robust stabilizability for a class of transfer functions" IEEE Trans. on Automatic Control, Vol.AC-29, pp.788-793, 1984

[8] M. Vidyasagar and H. Kimura, "Robust controllers for uncertain linear multivariable systems" Automatica, Vol.22, pp.85-94, 1986

[9] H. Maeda and M. Vidyasagar, "Design of multi-variable feedback systems with infinite gain margin and decoupling" Systems & Control Letters, Vol.6, pp.127-130, 1895

[10] H. Maeda and M. Vidyasagar, " Infinite gain margin problem in multivariable feedback systems" Automatica, Vol.22, pp.131-133, 1986

[11] H. Nogami, H. Maeda, M. Vidyadagar and S. Kodama, " Design of high gain feedback system with robust stability" Trans. of the Society of Instrument and Control Engineers, Vol.22, pp.1014-1020, 1986 (in Japanese)

[12] D.C. McFarlane and K. Glover, " Robust controller design using normalized coprime factor plant descriptions" Springer-Verlag, 1989

[13] J.C. Doyle, B. Francis and A. Tannenbaum, " Feedback control theory" Macmillan Publishing, 1992

[14] T. Iwasaki and R.E. Skelton, " All controllers for the general H1 control problem: LMI existence conditions and state space formulas" Automatica, Vol.30, pp.1307-1317, 1994

[15] P. Gahinet and P. Apkarian, " A linear matrix inequality approach to H1 control" International Journal of Robust and Nonlinear Control, Vol.4, pp.421-448, 1994

[16] K. Yamada and N. Matsushima, "A design method for Smith predictor for minimum phase time-delay plants", Proceedings of The 2005 Electrical Engineering/Electronics, Computer, Telecommunication, and Information Technology (ECTI) International Conference, Vol. I of II, Pattaya, Thailand, pp.347-350, 2005

[17] K. Yamada and N. Matsushima, "A design method for Smith predictors for minimum-phase time-delay plants"CECTI Transactions on Computer and Information Technology, Vol.2, No.2, pp.100-107, 2005

[18] K. Yamada, H. Takenaga, T. Hagiwara and H. Yamamoto, "A design method for Smith predictors for non-minimum-phase time-delay plants"Csubmitted for publication