The stability of input-output dynamical systems
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.
local and generalized principles of the argument
scientific article; zbMATH DE number 3865114