A class of absolutely stable distributed systems
type: Item
instance of: scholarly article
title: A class of absolutely stable distributed systems
zbMATH Open document ID: 0613.93048
published in: Automation and Remote Control
publication date: 1985-01-01T00:00:00Z
review text: The author studies a class of distributed systems which can be described by the equation \[ (1)\quad du/dt=Au+B\phi (Cu,t),\quad t\geq 0 \] where A is a closed linear operator which acts in a Hilbert space H, B and C are linear bounded operators which act from a Hilbert space E to H and from H to E respectively, \(\phi\) : \(E\times [0,\infty)\to E\) is a function that ensures the existence and uniqueness of a solution of equation (1) for any initial vector u(0), belonging to the domain of definition D(A) of the operator A, and that satisfies the inequality \[ | \phi (u,t)|_ E\leq q| u|_ E\quad (q=const;\quad t\geq 0) \] in which \(| \cdot |_ E\) denotes a norm on E. The author proves that if the linear part of (1) has an impulse function being in some sense positive, then the system (1) is absolutely stable in the Hurwitz' angle in the sense that the system satisfies the generalized hypothesis of absolute stability of dynamical systems in the Hurwitz' angle.
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93C25
Mathematics Subject Classification ID: 46C99
zbMATH DE Number: 3993418
zbMATH Keywords: distributed systems
zbMATH Keywords: Hilbert space
zbMATH Keywords: Hurwitz' angle
zbMATH Keywords: absolute stability
author: Michael I. Gil'
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3993418