Ebook: Stability and Stabilization of Infinite Dimensional Systems with Applications

The time evol11tion of many physical phenomena in nat11re can be de­ scribed by partial differential eq11ations. To analyze and control the dynamic behavior of s11ch systems. infinite dimensional system theory was developed and has been refined over the past several decades. In recent years. stim11lated by the applications arising from space exploration. a11tomated manufact11ring, and other areas of technological advancement, major progress has been made in both theory and control technology associated with infinite dimensional systems. For example, new conditions in the time domain and frequency domain have been derived which guarantee that a Co-semigroup is exponen­ tially stable; new feedback control laws helVe been proposed to exponentially ;;tabilize beam. wave, and thermoelastic equations; and new methods have been developed which allow us to show that the spectrum-determined growth condition holds for a wide class of systems. Therefore, there is a need for a reference book which presents these restllts in an integrated fashion. Complementing the existing books, e. g . . [1]. [41]. and [128]. this book reports some recent achievements in stability and feedback stabilization of infinite dimensional systems. In particular, emphasis will be placed on the second order partial differential equations. such as Euler-Bernoulli beam equations. which arise from control of numerous mechanical systems stich as flexible robot arms and large space structures. We will be focusing on new results. most of which are our own recently obtained research results.

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This book reports on recent achievements in stability and feedback stabilization of infinite systems. In particular emphasis is placed on second order partial differential equations, such as Euler-Bernoulli beam equations, which arise from vibration control of flexible robot arms and large space structures. 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. Proof procedures of existing theorems are simplified, and detailed proofs have been given to most theorems. In addition to benefiting from the presentation of new results on semigroups and their stability, readers can also learn several useful techniques for solving practical engineering problems. Until now, the recently obtained research results included in this book were unavailable in one volume. This self-contained book is an invaluable source of information for all those who are familiar with some basic theorems of functional analysis.

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This book reports on recent achievements in stability and feedback stabilization of infinite systems. In particular emphasis is placed on second order partial differential equations, such as Euler-Bernoulli beam equations, which arise from vibration control of flexible robot arms and large space structures. 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. Proof procedures of existing theorems are simplified, and detailed proofs have been given to most theorems. In addition to benefiting from the presentation of new results on semigroups and their stability, readers can also learn several useful techniques for solving practical engineering problems. Until now, the recently obtained research results included in this book were unavailable in one volume. This self-contained book is an invaluable source of information for all those who are familiar with some basic theorems of functional analysis.
Content:
Front Matter....Pages i-xiii
Introduction....Pages 1-14
Semigroups of Linear Operators....Pages 15-107
Stability of C 0-Semigroups....Pages 109-164
Static Sensor Feedback Stabilization of Euler-Bernoulli Beam Equations....Pages 165-257
Dynamic Boundary Control of Vibration Systems Based on Passivity....Pages 259-308
Other Applications....Pages 309-386
Back Matter....Pages 387-403

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This book reports on recent achievements in stability and feedback stabilization of infinite systems. In particular emphasis is placed on second order partial differential equations, such as Euler-Bernoulli beam equations, which arise from vibration control of flexible robot arms and large space structures. 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. Proof procedures of existing theorems are simplified, and detailed proofs have been given to most theorems. In addition to benefiting from the presentation of new results on semigroups and their stability, readers can also learn several useful techniques for solving practical engineering problems. Until now, the recently obtained research results included in this book were unavailable in one volume. This self-contained book is an invaluable source of information for all those who are familiar with some basic theorems of functional analysis.
Content:
Front Matter....Pages i-xiii
Introduction....Pages 1-14
Semigroups of Linear Operators....Pages 15-107
Stability of C 0-Semigroups....Pages 109-164
Static Sensor Feedback Stabilization of Euler-Bernoulli Beam Equations....Pages 165-257
Dynamic Boundary Control of Vibration Systems Based on Passivity....Pages 259-308
Other Applications....Pages 309-386
Back Matter....Pages 387-403
....