UID:
almafu_9958106763002883
Format:
1 online resource (171 p.)
ISBN:
1-282-03480-4
,
9786612034800
,
0-08-095998-9
Series Statement:
Mathematics in science and engineering ; v. 156
Content:
Functional Analysis and Linear Control Theory
Note:
Includes index.
,
Front Cover; Functional Analysis and Linear Control Theory; Copyright Page; Contents; Preface; Chapter 1. Preliminaries; 1.1 Control Theory; 1.2 Set Theory; 1.3 Linear Space (Vector Space); 1.4 Linear Independence; 1.5 Maximum and Supremum; 1.6 Metric and Norm; 1.7 Sequences and Limit Concepts; 1.8 Convex Sets; 1.9 Intervals on a Line; 1.10 The K Cube; 1.11 Product Sets and Product Spaces; 1.12 Direct Sum; 1.13 Functions and Mappings; 1.14 Exercises; Chapter 2. Basic Concepts; 2.1 Topological Concepts; 2.2 Compactness; 2.3 Convergence; 2.4 Measure Theory; 2.5 Euclidean Spaces
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2.6 Sequence Spaces2.7 The Lebesgue Integral; 2.8 Spaces of Lebesgue Integrable Functions (Lp Spaces); 2.9 Inclusion Relations between Sequence Spaces; 2.10 Inclusion Relations between Function Spaces on a Finite Interval; 2.11 The Hierarchy of Spaces; 2.12 Linear Functionals; 2.13 The Dual Space; 2.14 The Space of all Bounded Linear Mappings; 2.15 Exercises; Chapter 3. Inner Product Spaces and Some of their Properties; 3.1 Inner Product; 3.2 Orthogonality; 3.3 Hilbert Space; 3.4 The Parallelogram Law; 3.5 Theorems; 3.6. Exercises; Chapter 4. Some Major Theorems of Functional Analysis
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4.1 Introduction4.2 The Hahn-Banach Theorem and its Geometric Equivalent; 4.3 Other Theorems Related to Mappings; 4.4 Hölder's Inequality; 4.5 Norms on Product Spaces; 4.6 Exercises; Chapter 5. Linear Mappings and Reflexive Spaces; 5.1 Introduction; 5.2 Mappings of Finite Rank; 5.3 Mappings of Finite Rank on a Hilbert Space; 5.4 Reflexive Spaces; 5.5 Rotund Spaces; 5.6 Smooth Spaces; 5.7 Uniform Convexity; 5.8 Convergence in Norm (Strong Convergence); 5.9 Weak Convergence; 5.10 Weak Compactness; 5.11 Weak* Convergence and Weak* Compactness; 5.12 Weak Topologies
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5.13 Failure of Compactness in Infinite Dimensional Spaces5.14 Convergence of Operators; 5.15 Weak, Strong and Uniform Continuity; 5.16 Exercises; Chapter 6. Axiomatic Representation of Systems; 6.1 Introduction; 6.2 The Axioms; 6.3 Relation between the Axiomatic Representation and the Representation as a Finite Set of Differential Equations; 6.4 Visualization of the Concepts of this Chapter; 6.5 System Realization; 6.6 The Transition Matrix and Some of its Properties; 6.7 Calculation of the Transition Matrix for Time Invariant Systems; 6.8 Exercises
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Chapter 7. Stability, Controllability and Observability7.1 Introduction; 7.2 Stability; 7.3 Controllability and Observability; 7.4 Exercises; Chapter 8. Minimum Norm Control; 8.1 Introduction; 8.2 Minimum Norm Problems: Literature; 8.3 Minimum Norm Problems: Outline of the Approach; 8.4 Minimum Norm Problem in Hilbert Space: Definition; 8.5 Minimum Norm Problems in Banach Space; 8.6 More General Optimization Problems; 8.7 Minimum Norm Control: Characterization, a Simple Example; 8.8 Development of Numerical Methods for the Calculation of Minimum Norm Controls; 8.9 Exercises
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Chapter 9. Minimum Time Control
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English
Additional Edition:
ISBN 0-12-441880-5
Language:
English
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