The stability of input-output dynamical systems
type: Item
instance of: scholarly article
title: The stability of input-output dynamical systems
zbMATH Open document ID: 0543.93058
author: N. E. Zubov
published in: Mathematics in Science and Engineering
publication date: 1983-01-01T00:00:00Z
review text: This book develops necessary and sufficient conditions for input-output stability. Many results of the book are entirely new. - Chapter one contains necessary mathematical prelimaries of topology, as input-output stability is a topological concept defined on spaces of time functions. - Chapter two deals with a variety of local and generalized principles of the argument for complex polynomials with singular points and gives the associated encirclement conditions for multivariable systems. In chapter three the fundamental question of the representation of linear time-invariant operators and the concept of a transfer function is established. - In chapter four the authors combine the principle of the argument of chapter 2 and the representation theory of chapter 3 to obtain graphical criteria of the Nyquist type which are applicable in determining the stability of linear multivariable distributed feedback systems. The concepts of input-output stability are essentially based upon the existence of operators defined on Banach spaces, therefore in chapter five the authors consider in detail extended spaces. The concepts of causality, passivity, positivity and sectoricity are introduced in this chapter as a preliminary to their practical application in chapters six and seven.
Mathematics Subject Classification ID: 93D25
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 37C75
Mathematics Subject Classification ID: 47A67
Mathematics Subject Classification ID: 46B99
Mathematics Subject Classification ID: 30C15
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93C25
Mathematics Subject Classification ID: 93C35
zbMATH DE Number: 3865114
zbMATH Keywords: local and generalized principles of the argument
zbMATH Keywords: encirclement conditions
zbMATH Keywords: transfer function
zbMATH Keywords: feedback systems
zbMATH Keywords: Banach spaces
zbMATH Keywords: causality
zbMATH Keywords: passivity
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3865114