Optimization and Dynamical Systems
This work is aimed at mathematics and engineering graduate students and researchers in the areas of optimization, dynamical systems, control sys tems, signal processing, and linear algebra. The motivation for the results developed here arises from advanced engineering applications and the emer gen...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
London
Springer London
1994, 1994
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| Edition: | 1st ed. 1994 |
| Series: | Communications and Control Engineering
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- A.6 Eigenvalues, Eigenvectors and Trace
- A.7 Similar Matrices
- A.8 Positive Definite Matrices and Matrix Decompositions
- A.9 Norms of Vectors and Matrices
- A.10 Kronecker Product and Vec
- A.11 Differentiation and Integration
- A.12 Lemma of Lyapunov
- A.13 Vector Spaces and Subspaces
- A.14 Basis and Dimension
- A.15 Mappings and Linear Mappings
- A.16 Inner Products
- B Dynamical Systems
- B.1 Linear Dynamical Systems
- B.2 Linear Dynamical System Matrix Equations
- B.3 Controllability and Stabilizability
- B.4 Observability and Detectability
- B.5 Minimality
- B.6 Markov Parameters and Hankel Matrix
- B.7 Balanced Realizations
- B.8 Vector Fields and Flows
- B.9 Stability Concepts
- B.10 Lyapunov Stability
- C Global Analysis
- C.1 Point Set Topology
- C.2 Advanced Calculus
- C.3 Smooth Manifolds
- C.4 Spheres, Projective Spaces and Grassmannians
- C.5 Tangent Spaces and Tangent Maps
- C.6 Submanifolds
- C.7 Groups, Lie Groups and Lie Algebras
- C.8 Homogeneous Spaces
- C.9 Tangent Bundle
- C.10 Riemannian Metrics and Gradient Flows
- C.11 Stable Manifolds
- C.12 Convergence of Gradient Flows
- References
- Author Index
- 6.5 Flows on the Factors X and Y
- 6.6 Recursive Balancing Matrix Factorizations
- 7 Invariant Theory and System Balancing
- 7.1 Introduction
- 7.2 Plurisubharmonic Functions
- 7.3 The Azad-Loeb Theorem
- 7.4 Application to Balancing
- 7.5 Euclidean Norm Balancing
- 8 Balancing via Gradient Flows
- 8.1 Introduction
- 8.2 Flows on Positive Definite Matrices
- 8.3 Flows for Balancing Transformations
- 8.4 Balancing via Isodynamical Flows
- 8.5 Euclidean Norm Optimal Realizations
- 9 Sensitivity Optimization
- 9.1 A Sensitivity Minimizing Gradient Flow
- 9.2 Related L2-Sensitivity Minimization Flows
- 9.3 Recursive L2-Sensitivity Balancing
- 9.4 L2-Sensitivity Model Reduction
- 9.5 Sensitivity Minimization with Constraints
- A Linear Algebra
- A.1 Matrices and Vectors
- A.2 Addition and Multiplication of Matrices
- A.3Determinant and Rank of a Matrix
- A.4 Range Space, Kernel and Inverses
- A.5 Powers, Polynomials, Exponentials and Logarithms
- 1 Matrix Eigenvalue Methods
- 1.1 Introduction
- 1.2 Power Method for Diagonalization
- 1.3 The Rayleigh Quotient Gradient Flow
- 1.4 The QR Algorithm
- 1.5 Singular Value Decomposition (SVD)
- 1.6 Standard Least Squares Gradient Flows
- 2 Double Bracket Isospectral Flows
- 2.1 Double Bracket Flows for Diagonalization
- 2.2 Toda Flows and the Riccati Equation
- 2.3 Recursive Lie-Bracket Based Diagonalization
- 3 Singular Value Decomposition
- 3.1 SVD via Double Bracket Flows
- 3.2 A Gradient Flow Approach to SVD
- 4 Linear Programming
- 4.1 The Rôle of Double Bracket Flows
- 4.2 Interior Point Flows on a Polytope
- 4.3 Recursive Linear Programming/Sorting
- 5 Approximation and Control
- 5.1 Approximations by Lower Rank Matrices
- 5.2 The Polar Decomposition
- 5.3 Output Feedback Control
- 6 Balanced Matrix Factorizations
- 6.1 Introduction
- 6.2 Kempf-Ness Theorem
- 6.3 Global Analysis of Cost Functions
- 6.4 Flows for Balancing Transformations