NDLI: Robustly stable multivariate polynomials

Content Provider	Springer Nature Link
Author	Scheicher, Martin
Copyright Year	2011
Abstract	We consider stability and robust stability of polynomials with respect to a given arbitrary disjoint decomposition $${{\mathbb C}^{n} = \Gamma \uplus \Lambda }$$ . A polynomial is called stable if it has no zeros in the region of instability Λ and robustly stable if it is stable and remains so under small variations of its coefficients. Inspired by the article Robust stability of multivariate polynomials. Part 1: Small coefficient perturbations by Kharitonov et al. (Multidimens Syst Signal Process 10(1):21–32, 1999), we generalise some of their results to arbitrary stability decompositions and develop some fundamental results on robustly stable polynomials. The central one of them is a characterisation of robust stability in terms of the stability of several other polynomials, which yields a test for robust stability based on stability tests. Finally, we consider the special situation that the region of instability is a Cartesian product and recover some results for the standard stability decompositions for linear partial differential resp. difference equations with constant coefficients.
Ending Page	50
Page Count	28
Starting Page	23
File Format	PDF
ISSN	09236082
e-ISSN	15730824
Journal	Multidimensional Systems and Signal Processing
Issue Number	1
Volume Number	24
Language	English
Publisher	Springer US
Publisher Date	2011-05-08
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Robust stability Signal, Image and Speech Processing Artificial Intelligence (incl. Robotics) Arbitrary stability decomposition Multivariable systems Circuits and Systems Multivariate polynomials Electrical Engineering
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Artificial Intelligence Signal Processing Information Systems Computer Science Applications Software Hardware and Architecture

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