Theory of Stabilization for Linear Boundary Control Systems 1st Edition by Takao Nambu ISBN 1315350785 9781315350783

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ISBN 10: 1315350785 
ISBN 13: 9781315350783
Author: Takao Nambu

This book presents a unified algebraic approach to stabilization problems of linear boundary control systems with no assumption on finite-dimensional approximations to the original systems, such as the existence of the associated Riesz basis. A new proof of the stabilization result for linear systems of finite dimension is also presented, leading to an explicit design of the feedback scheme. The problem of output stabilization is discussed, and some interesting results are developed when the observability or the controllability conditions are not satisfied.

Theory of Stabilization for Linear Boundary Control Systems 1st Table of contents:

1 Preliminary results—Stabilization of linear systems of finite dimension
1.1 Introduction
1.2 Main results
1.3 Observability: Reduction to substructures
1.4 The case of a single observation
2 Preliminary results: Basic theory of elliptic operators
2.1 Introduction
2.2 Brief survey of Sobolev spaces
2.3 Elliptic boundary valule problems
2.3.1 The Dirichlet boundary
2.3.2 The Robin boundary
2.3.3 The case of a general boundary
2.3.4 On the domain of fractional powers Lcθ with Robinboundary
2.4 Analytic semigroup
3 Stabilization of linear systems of infinite dimension: Static feedback
3.1 Introduction
3.2 Decomposition of the system
3.3 Remark on the choice of the decay rate
3.4 Stability enhancement
3.5 Some generalization
4 Stabilization of linear systems of infinite dimension: Dynamic feedback
4.1 Introduction
4.2 Boundary Control Systems
4.3 Stabilization
4.4 Another Construction of Stabilizing Compensators
4.5 Alternative Framework of Stabilization
4.6 The Robin Boundary and Fractional Powers
4.7 Some Related Topics
4.7.1 On the growth rate of σ(Β)
4.7.2 On fractional powers of elliptic operators characterized by feedback boundary conditions
5 Stabilization of linear systems with Riesz Bases: Dynamic feedback
5.1 Introduction
5.2 Boundary Control Systems
5.3 Another Model of Identity Compensators
6 Output stabilization : lack of the observability and/or the controllability conditions
6.1 Introduction
6.2 Output stabilization
6.3 Application to boundary control systems
6.3.1 Algebraic approach to boundary control systems
6.3.2 Some generalization
6.4 Operator L admitting generalized eigenvectors
6.5 Some functionals
7 Stabilization of a class of linear control systems generating C0-semigroups
7.1 Introduction
7.2 Basic properties of the semigroup
7.3 Stabilization
8 A Computational Algorhism for an Infinite-Dimensional Sylvester’s Equation
8.1 Introduction
8.2 An algorhism

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Takao Nambu,Theory,Stabilization,Linear Boundary,Control Systems