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Original Articles

Robust stability and performance analysis of feedback control for plants with uncertain parameters in an ellipsoid

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Pages 537-548 | Received 21 May 1999, Accepted 30 Mar 2000, Published online: 03 Mar 2011

References

  • Anderson , B.D.O. , Kraus , F. J. , Mansour , M. and Dasgupta , S. 1995 . “Easily Testable Sufficient Conditions for Robust Stability of Systems with Multiaffine Parameter Dependence,” . Automatica , 31 ( 1 ) : 25 – 40 .
  • Barmish , B. R. and Kang , H. I. 1993 . “A Survey of Extreme Point Results for Robustness of Control Systems,” . Automatica , 29 ( 1 ) : 13 – 35 .
  • Barmish , B.R. 1984 . “Invariance of Strict Hurwitz Property of Polynomials with Perturbed Coefficients,” . IEEE Transactions on Automatic Control , 29 ( 10 ) : 935 – 936 .
  • Bartlett , A. C. , Hollot , C. V. and Huang , L. 1988 . “Root Locations of an Entire Polytope of Polynomials: It Suffice to Check the Edges,” . Mathematics of Control, Signals and Systems , 1 ( 1 ) : 61 – 71 .
  • Bhattacharyya , S. P. , Chapellat , H. and Keel , L. Hl . 1995 . Robust Control: The Parametric Approach , Upper Saddle River, NJ : Prentice Hall .
  • Bland , R. G. , Goldfarb , D. and Todd , M. J. 1981 . “The Ellipsoid Method: A Survey,” . Operations Research , 29 ( 6 ) : 1039 – 1091 .
  • Boese , F. G. 1994 . “An Auxiliary Theorem for Stability Analysis in the Presence of Interval‐valued Parameters,” . Multidimensional Systems and Signal Processing , 5 : 419 – 440 .
  • Chen , J. J. and Hwang , C. 1998 . “Robust D‐stability Analysis of Polynomial Families with Coefficients Depending Nonlinearly on Perturbed Parameters,” . IEE Proc.‐D: Control Theory and Applications , 145 ( 1 ) : 73 – 82 .
  • Crisalle , O. D. and Ballamudi , R. K. 1996 . “Robust Pole‐placement Technique for Plants with Ellipsoidally Uncertain Parameters,” . Chemical Engineering Science , 51 ( 12 ) : 3193 – 3202 .
  • Dahleh , M. , Tesi , A. and Vicino , A. 1993 . “An Overview of Extremal Properties for Robust Control of Interval Plants,” . Automatica , 29 ( 3 ) : 707 – 721 .
  • Frazer , R. A. and Duncan , W. J. 1929 . “On the Criteria for the Stability of Small Motion,” . Proc. Royal Society London A , 124 : 642 – 654 .
  • Hwang , C. and Chen , J. J. 1999 . “Plotting Robust Root Loci for Linear Systems with Multilinearly Parametric Uncertainties,” . International Journal of Control , (in press)
  • Hwang , C. , Chen , J. J. and Cheng , S. L. H8‐norm Computation for Linear Systems with Parameter Perturbations,” . Proc. of the 2nd IFAC Symposium on Robust Control Design . Budapest, Hungary. pp. 295 – 300 .
  • Jonckheere , E. A. and Ke , N. P. “Stability Margin Relative to Stratified Uncertainty Space, “ . Proc. of the 34th IEEE Conf. on Decision and Control . pp. 1322 – 1323 .
  • Kogan , J. 1995 . Robust Stability and Convexity , London : Springer‐Verlag .
  • Kogan , J. and Leizarowitz , A. 1995 . “Frequency Domain Criterion for Robust Stability of Interval Time‐delay Systems,” . Automatica , 31 ( 3 ) : 463 – 469 .
  • Mahon , H. M. and Crisalle , O. D. “On the Computation of the Robust Stability Margin for Ellipsoidal Parametric Uncertainties,” . Proc. of the American Control Conference . pp. 1439 – 1443 .
  • Milanese , M. and Vicino , A. 1991 . “Optimal Estimation Theory for Dynamic Systems with Set Membership Uncertainty: an Overview,” . Automatica , 27 : 997 – 1009 .
  • Polyak , B. T. 1992 . “Robustness Analysis for Multilinear Perturbations,” . In Robustness of Dynamic Systems with Parameter Uncertainties , Edited by: Mansour , M. 93 – 104 . Berlin : Birkhäuser .
  • Polyak , B. T. and Lan , L. H. 1996 . “Value Sets of Transfer Functions with Parametric Uncertainty and Their Applications in Robustness Analysis,” . (preprint)
  • Polyak , B. T. and Kogan , J. 1995 . “Necessary and Sufficient Conditions for Robust Stability of Linear Systems with Multiaffine Uncertainty Structure,” . IEEE Transactions on Automatic Control , 40 ( 7 ) : 1255 – 1260 .
  • Pronzato , L. and Walter , E. 1994 . “Minimum‐Volume Ellipsoids Containing Compact Sets: Application to Parameter Bounding,” . Automatica , 30 ( 11 ) : 1731 – 1739 .
  • Sobol , I. M. 1979 . “On the Systematic Search in a Hypercube,” . SIAM Journal on Numerical Analysis , 16 ( 5 ) : 790 – 793 .
  • Yamamura , K. and Sekiguchi , T. 1995 . “A Modified Spherical Method for Tracing Solution Curves,” . IEICE Transactions on Fundamentals , E78‐A ( 9 ) : 1233 – 1238 .
  • Yamamura , K. 1993 . “Simple Algorithms for Tracing Solution Curves,” . IEEE Transactions on Circuits and Systems , 40 ( 8 ) : 537 – 541 .
  • Zadeh , L. and Desoer , C. A. 1963 . Linear System Theory , New York, NY : McGraw‐Hill .
  • Correspondence addressee

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