Publication Cover
Applicable Analysis
An International Journal
Volume 52, 1994 - Issue 1-4
15
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Characterization of the stability radius via bifurcation techniques

Pages 231-245 | Received 31 Oct 1991, Published online: 02 May 2007

References

  • Biernacki , R.M. , Hwang , H. and Bhattacharyya , S.P. 1987 . Robust stability with structured real parameter perturbations, . Ieee Trans. Autom. Control Ac , 32 : 495 – 506 .
  • Brezzi , F. , Rappaz , J. and Raviart , P.A. 1981 . Finite dimensional approximations of nonlinear problems, . Part 11: Limit points, Numer. Math. , 37 : 1 – 28 .
  • Bunse–Gerstner , A. and Mehrmann , V. 1986 . A symplectic QR like algorithm for the solution of the real algebraic Riccati equation, . Ieee Trans. Autom. Control Ac , 31 : 1104 – 1113 .
  • Gantmacher , F.G. 1959 . The Theory of Matrices, , Vol. 1 , New York : Chelsea .
  • Hinrichsen , D. , Ilchmann , A. and Pritchard , A.J. 1989 . Robustness of stability of time-varying systems, . Journal Differ. Equations , 82 : 219 – 250 .
  • Hinrichsen , D. , Kelb , B. and Linnemann , A. 1987 . “ An algorithm for the computation of the structured stability radius with applications, ” . In Institut für Dynamische Systeme , Vol. 182 , Universität Bremen .
  • Hinrichsen , D. and Motscha , M. 1988 . “ Optimization problems of linear state space systems, ” . In Approximation and Optimization 59 – 78 . Springer Verlag, : LN Mathematics, .
  • Hinrichsen , D. and Pritchard , A.J. 1986 . Pritchard Stability radii of linear systems, . Syst. Control Lett. , 7 : 1 – 10 .
  • Hinrichsen , D. and Pritchard , A.J. 1986 . Stability radius for structural perturbations and the algebraic Riccati equation, . Syst. Control Lett. , 8 : 105 – 113 .
  • Hinrichsen , D. 1988 . “ An application of state space methods to obtain explicit formulae for robustness measures of polynomials ” . In Robustness in Identification and Control Torino
  • Hinrichsen , D. and Pritchard , A.J. Pritchard Robustness of stability of linear state space systems whith respect to time-varying, nonlinear and dynamic perturbations, .
  • Knobloch , H.W. and Kwakernaak , H. 1985 . Lineare Kontrolltheorie, Berlin et al : Springer-Verlag, .
  • Kubicek , M. and Marek , M. 1983 . “ Computational Methods in Bifurcation Theory and Dissipative Structures, ” . Berlin, : Springer-Verlag, .
  • Martin , J.M. and Hewer , G.A. 1987 . Hewer Smallest destabilizing perturbation for linear systems, . Int. J. Control , 45 : 1495 – 1504 .
  • Melhem , R.G. and Rheinboldt , W.C. 1982 . A comparison of methods for determining turning points of nonlinear equations, , 29 : 201 – 226 .
  • Moore , G. and Spence , A. 1988 . The calculation of turning points of nonlinear equations . SIAM J. Numer. Math. , 17 : 567 – 576 .
  • Pritchard , A.J. and Townley , S. 1989 . Robustness of linear systems, . Journal Differ. Equations , 77 : 254 – 286 .
  • Qui , L. and Davison , E.J. New perturbation bounds for the robust stability of linear state space models, . 751-755
  • Rheinboldt , W.C. 1986 . “ Numerical Analysis of Parametrized Nonlinear Equations, ” . New York : Wiley Interscience .
  • Spence , A. and Werner , B. 1982 . Nonsimple turning points and cusps, . IMA J. Numer. Anal. , 2 : 413 – 427 .
  • Van Loan , C. 1985 . How near is a stable matrix to an unstable matrix, . Contemporary Mathematics , : 466 – 478 .
  • Wonham , W.M. 1979 . “ Linear Multivariable Control: a Geometric Approach, ” . New York et al : Springer-Verlag .

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:

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:

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.