CFP last date
20 May 2024
Reseach Article

Hh Control of Discrete-time Uncertain Periodic Systems with Delays

by N. Bougatef, M. Chaabane, D. Mehdi
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 53 - Number 3
Year of Publication: 2012
Authors: N. Bougatef, M. Chaabane, D. Mehdi
10.5120/8405-2496

N. Bougatef, M. Chaabane, D. Mehdi . Hh Control of Discrete-time Uncertain Periodic Systems with Delays. International Journal of Computer Applications. 53, 3 ( September 2012), 45-51. DOI=10.5120/8405-2496

@article{ 10.5120/8405-2496,
author = { N. Bougatef, M. Chaabane, D. Mehdi },
title = { Hh Control of Discrete-time Uncertain Periodic Systems with Delays },
journal = { International Journal of Computer Applications },
issue_date = { September 2012 },
volume = { 53 },
number = { 3 },
month = { September },
year = { 2012 },
issn = { 0975-8887 },
pages = { 45-51 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume53/number3/8405-2496/ },
doi = { 10.5120/8405-2496 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:53:13.445390+05:30
%A N. Bougatef
%A M. Chaabane
%A D. Mehdi
%T Hh Control of Discrete-time Uncertain Periodic Systems with Delays
%J International Journal of Computer Applications
%@ 0975-8887
%V 53
%N 3
%P 45-51
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

This paper deals with the problem of H1 control for a class of linear discrete-time periodic system with delays. The obtained results are then extended for the time-delay periodic system with Linear Fractional Representation (LFR) uncertainty. Furthermore, linear matrix inequality (LMI)-based su cient conditions for H1 control are established. Two numerical examples are given to illustrate the applicability of the proposed approach.

References
  1. B. R. Barmish. Necessary and su cient conditions for qudratic stabilizability of an uncertain system. Journal of Optimization Theory and Applications, 46(4):399–408, 1985.
  2. S. W. Kau, Y. S. Liu, C. H. Lee, L. Hong, and C. H. Fang. An LMI approach to robust H1 control for uncertain continuoustime systems. Asian Journal of Control, 7(2):182–186, 2005.
  3. P. P. Khargonekar, I. Petersen, and K. Zhou. Robust stabilization of uncertain linear systems: quadratic stabilizability and H1 control theory. IEE Transaction on Automatic Control, 35(3):356–361, 1990.
  4. S. P. Shue P. Shi, E. K. Boukas and R. K. Agarwa. H1 control of discrete-time linear uncertain systems with delayed-state. In 37thConference on Decision and Control, pages 4551– 4552, Tampa, Florida USA, 1998.
  5. S. H. Song and J. K. Kim. H1 control of discrete-time linear systems with norm-bounded uncertainties and time delay in state. Automatica, 34(1):137–139, 1998.
  6. A. Stoorvogel. The H1 control problem. Systems and Control Engineering. Prentice Hall International (UK) Ltd, Eindhoven university of technology, 1992.
  7. M. Sun, Y. Jia, J. Du, and F. Yu. Robust h2/h1 control for time-delay systems with polytopic uncertainty. Asian Journal of Control, 11(1):11–20, 2009.
  8. L. Xie. Output feedback H1 control of systems with parameter uncertainty. International Journal of Control, 63(4):741– 750, 1996.
  9. L. Xie and C. E. De Souza. Robust H1 control for linear timeinvariant systems with norm-bounded uncertainty in the input matrix. Systems and Control Letters, 14:389–396, 1990.
  10. L. Xie and C. E. De Souza. Robust H1 control for linear systems with norm-bounded time-varying uncertainty. IEEE Transactions on Automatic Control, 37(8):1188–1191, 1992.
  11. S. Xu, J. Lam, and Y. Zou. Improved conditions for delaydependent robust stability and stabilization of uncertain discrete time-delay systems. Asian Journal of Control, 7(3):344– 348, 2005.
  12. L. Yuan, L. E. K. Achenie, and W. Jiang. Robust H1 control for linear discrete-time systems with norm-bounded timevarying uncertainty. Systems and Control Letters, 27:199– 208, 1996.
Index Terms

Computer Science
Information Sciences

Keywords

Discrete systems Periodic systems Time-delay State feedback stabilization Linear Fractional Representation H1 control Asymptotic stabilization robustness.