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.
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Acknowledgements
Dedicated to Professor Boris Polyak in honor of his 80th birthday.
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Mohsenizadeh, D.N., Oliveira, V.A., Keel, L.H., Bhattacharyya, S.P. (2016). Extremal Results for Algebraic Linear Interval Systems. In: Goldengorin, B. (eds) Optimization and Its Applications in Control and Data Sciences. Springer Optimization and Its Applications, vol 115. Springer, Cham. https://doi.org/10.1007/978-3-319-42056-1_12
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DOI: https://doi.org/10.1007/978-3-319-42056-1_12
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