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E-raamat: Theory of Stabilization for Linear Boundary Control Systems

(Kobe University, Japan)
  • Formaat: 284 pages
  • Ilmumisaeg: 03-Mar-2017
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781498758482
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Theory of Stabilization for Linear Boundary Control SystemsSuurem pilt
  • Formaat: 284 pages
  • Ilmumisaeg: 03-Mar-2017
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781498758482
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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.

Preface vii
1 Preliminary results---Stabilization of linear systems of finite dimension
1(26)
1.1 Introduction
1(5)
1.2 Main results
6(8)
1.3 Observability: Reduction to substructures
14(3)
1.4 The case of a single observation
17(10)
2 Preliminary results: Basic theory of elliptic operators
27(28)
2.1 Introduction
27(1)
2.2 Brief survey of Sobolev spaces
28(8)
2.3 Elliptic boundary valule problems
36(15)
2.3.1 The Dirichlet boundary
36(5)
2.3.2 The Robin boundary
41(2)
2.3.3 The case of a general boundary
43(5)
2.3.4 On the domain of fractional powers Leθ with Robinboundary
48(3)
2.4 Analytic semigroup
51(4)
3 Stabilization of linear systems of infinite dimension: Static feedback
55(38)
3.1 Introduction
55(4)
3.2 Decomposition of the system
59(5)
3.3 Remark on the choice of the decay rate
64(5)
3.4 Stability enhancement
69(9)
3.5 Some generalization
78(15)
4 Stabilization of linear systems of infinite dimension: Dynamic feedback
93(78)
4.1 Introduction
93(14)
4.2 Boundary Control Systems
107(6)
4.3 Stabilization
113(21)
4.4 Another Construction of Stabilizing Compensators
134(6)
4.5 Alternative Framework of Stabilization
140(12)
4.6 The Robin Boundary and Fractional Powers
152(7)
4.7 Some Related Topics
159(12)
4.7.1 On the growth rate of σ(B)
159(4)
4.7.2 On fractional powers of elliptic operators characterized by feedback boundary conditions
163(8)
5 Stabilization of linear systems with Riesz Bases: Dynamic feedback
171(22)
5.1 Introduction
171(2)
5.2 Boundary Control Systems
173(14)
5.3 Another Model of Identity Compensators
187(6)
6 Output stabilization: lack of the observability and/or the controllability conditions
193(30)
6.1 Introduction
193(3)
6.2 Output stabilization
196(6)
6.3 Application to boundary control systems
202(9)
6.3.1 Algebraic approach to boundary control systems
205(4)
6.3.2 Some generalization
209(2)
6.4 Operator L admitting generalized eigenvectors
211(1)
6.5 Some functionals
212(11)
7 Stabilization of a class of linear control systems generating Cθ-semigroups
223(24)
7.1 Introduction
223(2)
7.2 Basic properties of the semigroup
225(9)
7.3 Stabilization
234(13)
8 A Computational Algorhism for an Infinite-Dimensional Sylvester's Equation
247(18)
8.1 Introduction
247(4)
8.2 An algorhism
251(14)
References 265(6)
Index 271
Takao Nambu
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
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