Stability and inertia
type: Item
instance of: scholarly article
title: Stability and inertia
zbMATH Open document ID: 0972.15009
DOI: 10.1016/S0024-3795(99)00213-X
author: Biswa Nath Datta
published in: Linear Algebra and its Applications
publication date: 2000-06-07T00:00:00Z
review text: This is an excellent, clear and concise presentation of matrix stability and inertia theory, including generalized stability, and the application of these concepts to solutions of continuous and discrete problems. Succinct proofs and several open problems are given. The extensive bibliography documents the history and development of this subject, bringing together references from economics, control theory, mechanics, numerical analysis, and matrix theory. The Bézoutian and the dual concepts of controllability and observability are discussed and exploited. The classic Lyapunov and Stein theorems are proved, which characterize the stability of \(x'(t)= Ax(t)\) and \(x(k+1)= Ax(k)\) in terms of solutions to matrix equations. Subsequent extensions and related results are presented, bringing the theory up to date, and the interrelationships between theorems are explored. Some applications of inertia theory are presented, including root separation, D-stability, structural analysis and continued fractions. Numerical methods for determining stability and inertia are also discussed.
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 1419885
zbMATH Keywords: Lyapunov stability
zbMATH Keywords: matrix stability
zbMATH Keywords: inertia theory
zbMATH Keywords: bibliography
zbMATH Keywords: controllability
zbMATH Keywords: observability
zbMATH Keywords: matrix equations
zbMATH Keywords: root separation
zbMATH Keywords: D-stability
MaRDI profile type: Publication
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