NDLI: A practical, computationally aware vertex solution for checking robust stability of 'structured' convex combinations of matrices

Content Provider	IEEE Xplore Digital Library
Author	Yedavalli, R.K.
Copyright Year	2006
Description	Author affiliation: Fac. of Aerosp. Eng., Ohio State Univ., Columbus, OH (Yedavalli, R.K.)
Abstract	This paper presents a practical, computationally aware 'vertex solution' to the problem of checking the stability of families of matrices described by convex combinations of Hurwitz stable 'vertex' matrices. The convex combinations resulting from the interval parameter matrix family are labeled as 'structured' convex combinations to distinguish them from the so called 'unstructured' convex combinations which are convex combinations of 'user specified' Hurwitz stable vertex matrices. A previously presented 'vertex algorithm' by the author for this tough problem is derived under the 'conceptual' assumption of a 'closed, connected complex plane'. Later, upon realizing that a 'practical' computational environment assumes an 'open, unconnected complex plane', a computationally aware vertex solution is offered which accounts for the 'discrepancy' in the results for some 'ill-conditioned' problems because the eigenvalues which are supposed to be residing in a closed, connected complex plane are calculated using methods meant for open, unconnected complex plane. This 'discrepancy' arises for some ill-conditioned problems because in an open, unconnected complex plane, the theoretically present coupling between real eigenvalues and complex (real part) eigenvalues, is destroyed. In this paper, this 'practical, computationally aware' algorithm is presented in its 'final' form by carefully highlighting differences between a 'conceptual' solution and the 'real world, practical' solution. This in turn clarifies the reason why this problem has been a 'tough nut to crack' over all these years. Several examples are given which clearly demonstrate effectiveness of the new algorithm, even for ill-conditioned problems. It is hoped that this 'final' solution paves the way for continued interest in the research related to this important area with many applications
Sponsorship	American Automatic Control Council IFAC
File Size	305138
File Format	PDF
ISBN	1424402093
e-ISBN	1424402107
DOI	10.1109/ACC.2006.1657529
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-06-14
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	American Automatic Control Council(AACC)
Subject Keyword	Robust stability Eigenvalues and eigenfunctions Stability analysis State-space methods Vectors Robust control Control theory Aerospace engineering Uncertainty
Content Type	Text
Resource Type	Article

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