Advanced search
Publication Cover
International Journal of Control Volume 75, 2002 - Issue 13
Submit an article Journal homepage
109
Views
12
CrossRef citations to date
0
Altmetric
Original Articles

Optimal control of discrete-time singularly perturbed systems

M. Bidani
,
N. E. Radhy
&
B. Bensassi
Pages 955-966 | Published online: 08 Nov 2010

  • BIALKOWSH , W. L. Application of steady state Kaiman filters-theory with field results . Proceedings of the Joint Automatic Control Conference . October 18 , Philadelphia, USA.
  • BLANKENSHIP , G. 1981 . Singularly perturbed difference equations in optimal control problems . IEEE Transactions on Automatic Control , 26 : 911 – 917 .
  • BUTUZOV , V. and VASILEVA , A. 1971 . Differential and difference equation systems with a small parameter for the case in which the unperturbed (singular) system is in the spectrum . Journal of Differential Equations , 6 : 499 – 510 .
  • CHANG , K. 1972 . Singular perturbation of a general boundary value problem . SIAM Journal on Mathematical Analysis , 3 : 520 – 526 .
  • COLANERl , P. , SCATTOLINl , R. and SCHIAVON , N. 1992 . LQG optimal control of multirate sampled-data systems . IEEE Transactions on Automatic Control , 37 : 675 – 682 .
  • DERBEL , N. , MOHAMED KAMOUN , B. A. and POLOUJADOFF , M. 1994 . New approach to block-diagonalization of singularly perturbed systems by Taylor expansion . IEEE Transactions on Automatic Control , 39 : 1429 – 1431 .
  • ELGARD , I. O. and FOSHA , E. C. 1970 . Optimum megawattfrequency control of multiarea electric energy systems . IEEE Transactions on Power Apparatus and Systems , 89 : 556 – 563 .
  • ESFANDIARI , F. and KHALIL , H. K. 1939 . On the robustness of sampled-data control to unmodeled high-frequency dynamics . IEEE Transactions on Automatic Control , 34 : 900 – 903 .
  • GAJIC , Z. , LIM , M. T. and SHEN , X. 1995 . “ The study of discrete singularly perturbed linear-quadratic control systems ” . In Control and Dynamic Systems: Advances in Theory and Application , Edited by: Leondes , C. T. Vol. 70 , 199 – 242 . San Diego : Academic Press .
  • GAJIC , Z. and QURESHI , M. 1995 . Lyapunov Matrix Equation in Systems Stability and Control , San Diego : Academic Press .
  • GAJIC , Z. and SHEN , X. 1991 . study of the discrete singularly perturbed linear-quadratic control problem by a bilinear transformation . Automatica , 27 : 1025 – 1028 .
  • HOPPENSTEADT , F. and MIRANKER , W. 1977 . Multi-time methods for systems of difference equations . Studies in Applied Mathematics , 56 : 273 – 298 .
  • KECMAN , V. , BINGULAC , S. and GAJIC , Z. 1999 . Eigenvector approach for order reduction of singularly perturbed linearquadratic optimal control problems . Automatica , 35 : 151 – 158 .
  • KHORASANI , K. and AZIMI-SADJADI , M. 1937 . Feedback control of two-time scale block implemented discrete-time systems . IEEE Transactions on Automatic Control , 32 : 69 – 73 .
  • KOKOTOVIC , P. , ALLEMONG , J. and CHOW , J. 1980 . Singular perturbations and iterative separation of time scales . Automatica , 16 : 23 – 33 .
  • KOKOTOVIC , P. , KHALIL , H. K. and O'REILLY , J. 1986 . Singular Perturbation Methods in Control: Analysis and Design , London : Academic Press .
  • LAUB , A. J. 1979 . A Schur method for solving algebraic Riccati equations . IEEE Transactions on Automatic Control , 24 : 913 – 921 .
  • LIM , M. T. , GAJIV , Z. and SHEN , X. New methods for optimal control and filtering of singularly perturbed linear discrete stochastic systems . Proceedings of the American Control Conference . June , Seattle, WA, USA. pp. 534 – 538 .
  • LITKOUHI , B. 1983 . “ Sampled-data control of systems with slow and fast models ” . 48824 – 51229 . East Lansing, MI, , USA : University of Michigan . PhD thesis
  • LITKOUHI , B. and KHALIL , H. K. 1934 . Infinite-time regulators for singularly perturbed difference equations . International Journal of Control , 39 : 587 – 598 .
  • LITKOUHI , B. and KHALIL , H. K. 1935 . Multirate and composite control of two-time-scale discrete systems . IEEE Transactions on Automatic Control , 30 : 645 – 651 .
  • MAHMOUD , M. 1986 . Stabilization of discrete systems with multiple-time scales . IEEE Transactions on Automatic Control , 31 : 159 – 162 .
  • MAHMOUD , M. , CHEN , Y. and SINGH , M. 1936 . Discrete two-time-scale systems . International Journal of Systems Science , 17 : 1187 – 1207 .
  • NAIDU , D. S. and KAILLASA RAO , A. 1935 . Singular Perturbation Analysis of Discrete Control Systems, Lecture Notes in Mathematics , Berlin : Springer-Verlag .
  • OLOOMI , H. and SAWAN , M. 1937 . The observer-based controller design of discrete-time singularly perturbed systems . IEEE Transactions on Automatic Control , 32 : 246 – 248 .
  • ORTEGA , J. and RHEINBOLDT , W. 1970 . Iterative Solution of Nonlinear Equations on Several Variables , New York : Academic Press .
  • PAPPAS , T. , LAUB , A. J. and SANDELL , N. R. 1980 . On the numerical solution of the discrete-time algebraic Riccati equation . IEEE Transactions on Automatic Control , 25 : 631 – 641 .
  • PHILLIPS , R. 1980 . Reduced order modeling and control of two-time-scale discrete control systems . International Journal of Control , 31 : 761 – 780 .
  • Su , W. , GAJIC , Z. and SHEN , X. 1992 . The exact slow-fast decomposition of the algebraic Riccati equation of singularly perturbed systems . IEEE Transactions on Automatic Control , 37 : 1456 – 1459 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.