Stability and stabilization of infinite dimensional systems with applications
type: Item
instance of: scholarly article
title: Stability and stabilization of infinite dimensional systems with applications
zbMATH Open document ID: 0922.93001
author: Zhenghua Luo
author: Bao-Zhu Guo
author: Ömer Morgül
published in: Communications and Control Engineering
publication date: 1999-05-04T00:00:00Z
review text: The time evolution of many physical phenomena in nature can be described by partial differential equations. In this very important book, the authors concentrate on the analysis and control of the dynamic behavior of such systems. The book reports upon some recent achievements in stability and feedback stabilization of infinite dimensional systems, with the emphasis on the second order partial differential equations which arise from the control of numerous mechanical systems such as flexible robot arms and large space structures. A number of new features obtained by the authors include: The integrated semigroup theory, the theorems and characterizations on weak strong stabilities of \(C_0\)-semigroups and a new characterization of the growth rate of a \(C_0\)-semigroup, the \(A\)-dependent operator concept, which has proven to be a powerful tool for establishing the well-posedness of some non-standard abstract second order equations, the application of the energy multiplier method to the proof of the closed-loop stability of beam equations with dynamic boundary control, the exponential stability analysis for a wide class of systems with boundary stabilizers, based on the verification of the spectrum-determined growth condition. It is the authors' aim to introduce the reader to this very important research field and to some of its applications. Detailed proofs for most lemmas and theorems are given. The book is thus adequate as a textbook for students in applied mathematics or as a reference book for control engineers and applied mathematicians interested in the analysis and control of infinite dimensional systems. The book presents not only some new theorems on semigroups and their stability but also some useful techniques for solving practical engineering problems.
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 93C25
Mathematics Subject Classification ID: 74M05
Mathematics Subject Classification ID: 74K10
zbMATH DE Number: 1284519
zbMATH Keywords: static sensor
zbMATH Keywords: Euler-Bernoulli beam
zbMATH Keywords: control of vibration systems
zbMATH Keywords: passivity
zbMATH Keywords: stabilities of \(C_0\)-semigroups
zbMATH Keywords: \(A\)-dependent operator concept
zbMATH Keywords: feedback stabilization
zbMATH Keywords: infinite dimensional systems
zbMATH Keywords: second order partial differential equations
zbMATH Keywords: flexible robot arms
zbMATH Keywords: large space structures
zbMATH Keywords: semigroup theory
zbMATH Keywords: well-posedness
zbMATH Keywords: energy multiplier method
zbMATH Keywords: dynamic boundary control
reviewed by: Jan Lovíšek
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1284519