On boundary implications of stability and positivity properties of multidimensional systems

Author

Basu, Sankar

Author_Institution

Lab. for Inf. & Decision Syst., MIT, Cambridge, MA, USA

Volume

78

Issue

4

fYear

1990

fDate

4/1/1990 12:00:00 AM

Firstpage

614

Lastpage

626

Abstract

Multidimensional generalizations of various 1-D results on the robustness of Hurwitz, Schur, and positivity properties of polynomials and rational functions are considered. More specifically, the convexity property of the stable region in the coefficient space of multivariable polynomials is studied. Multidimensional generalizations of Kharitonov-type results are reviewed, and further extensions, including that of the 1-D edge theorem, are discussed. Interval positivity properties of multivariate rational functions are characterized in terms of ratios of a finite number of Kharitonov-type polynomials constructed from the extreme values of the intervals of perturbation

Keywords

multidimensional systems; polynomials; stability; 1-D edge theorem; Hurwitz; Kharitonov-type results; Schur; coefficient space; convexity property; multidimensional systems; multivariable polynomials; perturbation; polynomials; positivity; rational functions; robustness; stability; stable region; Adaptive filters; Convergence; Digital filters; Explosions; Multidimensional signal processing; Multidimensional systems; Passive networks; Polynomials; Robust stability; Robustness;

fLanguage

English

Journal_Title

Proceedings of the IEEE

Publisher

ieee

ISSN

0018-9219

Type

jour

DOI

10.1109/5.54802

Filename

54802