Stability and Stabilization of Infinite Dimensional Systems with Applications

AvZheng-Hua Luo,Bao-Zhu Guo

Häftad, Engelska, 2012

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Beskrivning

This book reports on recent achievements in stability and feedback stabilization of infinite systems. Various control methods such as sensor feedback control and dynamic boundary control are applied to stabilize the equations. Many new theorems and methods are included in the book.

Produktinformation

Utgivningsdatum:2012-10-08
Mått:155 x 235 x 22 mm
Vikt:590 g
Format:Häftad
Språk:Engelska
Serie:Communications and Control Engineering
Antal sidor:403
Förlag:Springer London Ltd
ISBN:9781447111368

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Innehållsförteckning

1 Introduction.- 1.1 Overview and examples of infinite dimensional systems.- 1.2 Organization and brief summary.- 1.3 Remarks on notation.- 1.4 Notes and references.- 2 Semigroups of Linear Operators.- 2.1 Motivation and definitions.- 2.2 Properties of semigroups.- 2.3 Generation theorems for semigroups.- 2.4 Relation with the Laplace transform.- 2.5 Differentiability and analytic semigroups.- 2.6 Compact semigroups.- 2.7 Abstract Cauchy problem.- 2.8 Integrated semigroups.- 2.9 Nonlinear semigroups of contractions.- 2.10 Notes and references.- 3 Stability of C0-Semigroups.- 3.1 Spectral mapping theorems.- 3.2 Spectrum-determined growth condition.- 3.3 Weak stability and asymptotic stability.- 3.4 Exponential stability — time domain criteria.- 3.5 Exponential stability — frequency domain criteria.- 3.6 Essential spectrum and compact perturbations.- 3.7 Invariance principle for nonlinear semigroups.- 3.8 Notes and references.- 4 Static Sensor Feedback Stabilization of Euler-Bernoulli Beam Equations.- 4.1 Modeling of a rotating beam with a rigid tip body.- 4.2 Stabilization using strain or shear force feedback.- 4.3 Damped second order systems.- 4.4 Exponential stability and spectral analysis.- 4.5 Shear force feedback control of a rotating beam.- 4.6 Stability analysis of a hybrid system.- 4.7 Gain adaptive strain feedback control of Euler-Bernoulli beams.- 4.8 Notes and references.- 5 Dynamic Boundary Control of Vibration Systems Based on Passivity.- 5.1 A general framework for system passivity.- 5.2 Dynamic boundary control using positive real controllers.- 5.3 Dynamic boundary control of a rotating flexible beam.- 5.4 Stability robustness against small time delays.- 5.5 Notes and references.- 6 Other Applications.- 6.1 A General linear hyperbolic system.- 6.2 Stabilization of serially connected vibrating strings.- 6.3 Two coupled vibrating strings.- 6.4 A vibration cable with a tip mass.- 6.5 Thermoelastic system with Dirichlet — Dirichlet boundary conditions.- 6.6 Thermoelastic system with Dirichlet — Neumann boundary conditions.- 6.7 Renardy’s counter-example on spectrum-determined growth condition.- 6.8 Notes and references.