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Extremal Results for Algebraic Linear Interval Systems

In: Optimization and Its Applications in Control and Data Sciences

Author

Listed:
  • Daniel N. Mohsenizadeh

    (Texas A&M University)

  • Vilma A. Oliveira

    (University of Sao Paulo at Sao Carlos)

  • Lee H. Keel

    (Tennessee State University)

  • Shankar P. Bhattacharyya

    (Texas A&M University)

Abstract

This chapter explores some important characteristics of algebraic linear systems containing interval parameters. Applying the Cramer’s rule, a parametrized solution of a linear system can be expressed as the ratio of two determinants. We show that these determinants can be expanded as multivariate polynomial functions of the parameters. In many practical problems, the parameters in the system characteristic matrix appear with rank one, resulting in a rational multilinear form for the parametrized solutions. These rational multilinear functions are monotonic with respect to each parameter. This monotonic characteristic plays an important role in the analysis and design of algebraic linear interval systems in which the parameters appear with rank one. In particular, the extremal values of the parametrized solutions over the box of interval parameters occur at the vertices of the box.

Suggested Citation

  • Daniel N. Mohsenizadeh & Vilma A. Oliveira & Lee H. Keel & Shankar P. Bhattacharyya, 2016. "Extremal Results for Algebraic Linear Interval Systems," Springer Optimization and Its Applications, in: Boris Goldengorin (ed.), Optimization and Its Applications in Control and Data Sciences, pages 341-351, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-42056-1_12
    DOI: 10.1007/978-3-319-42056-1_12
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