Robust Stability Condition for a Class of Time-Delay Plants with Uncertainty
Main Article Content
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
This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge.
- Creative Commons Copyright License
The journal allows readers to download and share all published articles as long as they properly cite such articles; however, they cannot change them or use them commercially. This is classified as CC BY-NC-ND for the creative commons license.
- Retention of Copyright and Publishing Rights
The journal allows the authors of the published articles to hold copyrights and publishing rights without restrictions.
References
[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