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Robust control of interval systems

  • L. H. Keel
  • J. Shaw
  • S. P. Bhattacharyya
Conference paper
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 183)

Abstract

In this paper we consider a feedback interconnection of two linear time invariant systems, one of which is fixed and the other is uncertain with the uncertainty being a box in the space of coefficients of the numerator and denominator polynomials. This kind of system arises in robust control analysis and design problems. We give several results for the Nyquist plots and stability margins of such families of systems based on the extremal segments of rational functions introduced by Chapellat and Bhattacharyya [1]. These CB segments play a fundamental characterizing role in many control design problems.

Keywords

Nyquist Plot Stability Margin Linear Time Invariant System Interval System Interval Polynomial 
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References

  1. [1]
    H. Chapellat and S. P. Bhattacharyya, “A generalization of Kharitonov's theorem: robust stability of interval plants,” IEEE Transactions on Automatic Control, vol. AC-34, pp. 306–311, March 1989.CrossRefMathSciNetGoogle Scholar
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    V. L. Kharitonov, “Asymptotic stability of an equilibrium position of a family of systems of linear differential equations,” Differential Uravnen, vol. 14, pp. 2086–2088, 1978.zbMATHMathSciNetGoogle Scholar
  3. [3]
    H. Chapellat, M. Dahleh, and S. P. Bhattacharyya, “Robust stability under structured and unstructured perturbations,” IEEE Transactions on Automatic Control, vol. AC-35, pp. 1100–1108, October 1990.Google Scholar
  4. [4]
    H. Chapellat, M. Dahleh, and S. Bhattacharyya, “Extremal manifolds in robust stability,” TCSP Report, Texas A&M University, July 1990.Google Scholar
  5. [5]
    L. Keel, J. Shaw and S. P. Bhattacharyya, “Frequency domain design of interval control systems,” Tech. Rep., Tennessee State University, July 1991. Also in TCSP Tech. Rep., Texas A&M University, July 1991.Google Scholar
  6. [6]
    A. Tesi and A. Vicino, “Kharitonov segments suffice for frequency response analysis of plant-controller families”. To appear in Control of Uncertain Dynamic Systems, September 1991, CRC Press.Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • L. H. Keel
    • 1
  • J. Shaw
    • 2
  • S. P. Bhattacharyya
    • 2
  1. 1.Center of Excellence in Information SystemsTennessee State UniversityNashvilleU.S.A
  2. 2.Department of Electrical EngineeringTexas A&M UniversityCollege StationU.S.A.

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