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Nederlands Buitenlands   Alles  Titel  Auteur  ISBN        
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J. R. Leigh

Functional Analysis and Linear Control Theory

€ 13.95



Taal / Language : English

Inhoudsopgave:
Preface to the Dover Edition iv
Preface v
CHAPTER 1. Preliminaries 1
Control Theory.
Set Theory.
Linear Space (Vector Space).
Linear Independence.
Maximum and Supremum.
Metric and Norm.
Sequence and Limit Concepts.
Convex Sets.
Intervals on a Line.
The k Cube.
Product Sets and Product Spaces.
Direct Sum.
Functions and Mappings.
Exercises.
CHAPTER 2. Basic Concepts 11
Topological Concepts.
Compactness.
Convergence.
Measure Theory.
Euclidean Spaces.
Sequence Spaces.
The Lebesgue Integral.
Spaces of Lebesque Integrable Functions (LP Spaces).
Inclusion Relations between Sequence Spaces.
Inclusion Relations between Function Spaces on a Finite Interval.
The Hierarchy of Spaces.
Linear Functionals.
The Dual Space.
The Space of all Bounded Linear Mappings.
Exercises.
CHAPTER 3. Inner Product Spaces and Some of their Properties 26
Inner Product.
Orthogonality.
Hilbert Space.
The Parallelogram Law.
Theorems.
Exercises.
CHAPTER 4. Some Major Theorems of Functional Analysis 33
Introduction.
The Hahn Banach Theorem and its Geometric Equivalent.
Other Theorems Related to Mappings.
Holder`s Inequality.
Norms on Product Spaces.
Exercises.
CHAPTER 5. Linear Mappings and Reflexive Spaces 41
Introduction.
Mappings of Finite Rank.
Mappings of Finite Rank on a Hilbert Space.
Reflexive Spaces.
Rotund Spaces.
Smooth Spaces.
Uniform Convexity.
Convergence in Norm (Strong Convergence).
Weak Convergence.
Weak Compactness.
Weak Convergence and Weak Compactness.
Weak Topologies.
Failure of Compactness in Infinite Dimensional Spaces.
Convergence of Operators.
Weak, Strong and Uniform Continuity.
Exercises.
CHAPTER 6. Axiomatic Representation of Systems 50
Introduction.
The Axioms.
Relation between the Axiomatic Representation and the Representation as a Finite Set of Differential Equations.
Visualization of the Concepts of this Chapter.
System Realization.
The Transition Matrix and some of its Properties.
Calculation of the Transition Matrix for Time Invariant Systems.
Exercises.
CHAPTER 7. Stability, Controllability and Observability 63
Introduction.
Stability.
Controllability and Observability.
Exercises.
CHAPTER 8. Minimum Norm Control 79
Introduction.
Minimum Norm Problems: Literature, Outline of the Approach.
Minimum Norm Problem in Hilbert Space: Definition.
Minimum Norm Problems in Banach Space.
More General Optimization Problems.
Minimum Norm Control: Characterization, a Simple Example.
Development of Numerical Methods for the Calculation of Minimum Norm Controls.
Exercises.
CHAPTER 9. Minimum Time Control 103
Preliminaries and Problem Description.
The Attainable Set.
Existence of a Minimum Time Control.
Uniqueness.
Characterization.
The Pontryagin Maximum Principle.
Time Optimal Control.
Exercises.
CHAPTER 10. Distributed Systems 120
Introduction.
Further Theorems from Functional Analysis.
Axiomatic Description.
Representation of Distributed Systems.
Characterization of the Solution of the Equation z = Ax + Bu.
Stability.
Controllability.
Minimum Norm Control.
Time Optimal Control.
Optimal Control of a Distributed System: An Example.
Approximate Numerical Solution.
Exercises.
Glossary of Symbols 141
References and Further Reading 145
Subject Index 157
About the Author 161
Extra informatie: 
Paperback / softback
160 pagina's
Januari 2007
186 gram
216 x 143 x 9 mm
DOVER PUBN INC us


Levertijd: 5 tot 11 werkdagen