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 robots 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.
New results on semigroups and their stability are presented, and readers can 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.
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 splĂ&
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