http://iet.metastore.ingenta.com
1887

Stability margins of diagonally perturbed multivariable feedback systems

Stability margins of diagonally perturbed multivariable feedback systems

For access to this article, please select a purchase option:

Buy article PDF
$19.95
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IEE Proceedings D (Control Theory and Applications) — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

For diagonally perturbed linear time-invariant multivariable feedback systems, the problem of finding an improved characterisation of the stability margin is examined. A readily computable lower bound for diagonally perturbed systems is developed using Perron-Frobenius non-negative matrix results. The present theory improves upon the existing singular-value stability-margin theory, providing a simple constructive method for determining previously unspecified norm weighting parameters (i.e. scaling factors) so as to minimise the conservativeness of stability-margin bounds.

References

    1. 1)
      • Barrett, M.F.: `Conservatism with robustness tests for linear feedback control systems', June 1980, Ph.D. thesis, University of Minnesota, USA, report 80SRC35, Honeywell Systems Research Center, Minneapolis, Minnesota, USA.
    2. 2)
      • G. Stein , N.R. Sandell . (1979) , Classical and modern methods for control system design.
    3. 3)
      • Safonov, M.G., Athans, M.: `A multiloop generalisation of the circle stability criterion', Proceedings of twelfth annual Asilomar conference on circuits, systems and computers, November 1978, California, USA, Pacific Grove.
    4. 4)
      • Doyle, J.C.: `Robustness of multiloop linear feedback systems', Proceedings of IEEE conference on decision and control, december 1979, Fort Lauderdale, Florida, USA.
    5. 5)
      • M.G. Safonov , M. Athans . A multiloop generalisation of the circle criterion for stability margin analysis. IEEE Trans. , 415 - 422
    6. 6)
      • N.R. Sandell . Robust stability of systems with application to singular perturbations. Automatica , 467 - 470
    7. 7)
      • I. Postlethwaite , J.M. Edmunds , A.G.J. MacFarlane . Principal gains and phases in the analysis of linear multivariable feedback systems. IEEE Trans. , 32 - 46
    8. 8)
      • M.G. Safonov , A.J. Laub , G.L. Hartmann . Feedback properties of multivariable systems: The role and use of the return difference matrix. IEEE Trans. , 75 - 92
    9. 9)
      • N.A. Lehtomaki , N.R. Sandell , M. Athans . Robustness results in linear-quadratic Gaussian based multivariable control designs. IEEE Trans. , 75 - 92
    10. 10)
      • Barrett, M.R.: `Conservatism with robustness tests for linear feedback control systems', Proceedings of IEEE conference on decision and control, December 1980, Albuquerque, New Mexico, USA.
    11. 11)
      • J.C. Doyle , G. Stein . Multivariable feedback system desigh Concepts for a classical modern synthesis. IEEE Trans. , 4 - 16
    12. 12)
      • H.H. Rosenbrock , P.A. Cook . Stability and the eigenvalues of G(s). Int. J. Control , 99 - 104
    13. 13)
      • M.G. Safonou , M. Athans . Gain and phase margin for multi loop LQG regulators. IEEE Trans. , 173 - 178
    14. 14)
      • Safonov, M.G.: `Robustness and stability aspects of stochastic multivariable feedback system design', August 1977, Ph.D. thesis, MIT, Cambridge, Massachusetts, USA, report ESL-R-763, Electronics Systems Laboratory, MIT, Cambridge, Massachusetts, USA, Sept. 1977.
    15. 15)
      • F.M. Callier , W.S. Chan , C.A. Desoer . Input-output stability of interconnected systems using decompositios: An improved formultion. IEEE Trans. , 150 - 163
    16. 16)
      • M. Araki . Input-output stability of composite feedback systems. IEEE Trans. , 254 - 259
    17. 17)
      • F.R. Gantmacher . (1959) , Theory of matrices.
    18. 18)
      • A.J. Mees . Achieving diagonal dominance. Syst. Control Lett. , 155 - 158
    19. 19)
      • E.E. Osborne . On preconditioning of matrices. J. Assoc. Comput. Mach. , 338 - 345
    20. 20)
      • J. Wilkinson . (1965) , Algebraic eigenvalue problem.
    21. 21)
      • J. Stoer , C. Witzgall . Transformations by diagonal matrices in a normed space. Nimer. Math. , 458 - 471
    22. 22)
      • F.L. Bauer . Optimally scaled matrices. Nimer. Math. , 73 - 87
http://iet.metastore.ingenta.com/content/journals/10.1049/ip-d.1982.0054
Loading

Related content

content/journals/10.1049/ip-d.1982.0054
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address