Computational Aspects of Linear Control

AvClaude Brezinski

Inbunden, Engelska, 2002

Del i serien Numerical Methods and Algorithms

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Beskrivning

The main objective of this volume is to create a bridge between control theory and its numerical analysis aspects. The book combines an exposition of linear control theory and the corresponding modern relevant computational techniques such as orthogonal polynomials, Pade approximation, numerical linear algebra, and some topics on nonlinear differential equations. It can be considered as an introduction to control theory for numerical analysts looking for a wide area of applications and as an introduction to recent numerical methods for control specialists.

Produktinformation

Utgivningsdatum:2002-06-30
Mått:155 x 235 x 19 mm
Vikt:610 g
Format:Inbunden
Språk:Engelska
Serie:Numerical Methods and Algorithms
Antal sidor:295
Upplaga:2002
Förlag:Kluwer Academic Publishers
ISBN:9781402007118

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Recensioner i media

From the reviews: "[...]there are very few books, if any, which combine control theory and relevant numerical techniques. The present book under review, Computational Aspects of Linear Control, by Claude Brezinski, is exactly such a book." (Ezra Zeheb, Technion-Israel Institute of Technology)

Innehållsförteckning

1. Control of Linear Systems.- 1 The control problem.- 2 Examples.- 3 Basic notions and results.- 4 Controllability.- 5 Observability.- 6 The canonical representation.- 7 Realization.- 8 Model reduction.- 9 Stability analysis.- 10 Poles and zeros.- 11 Decoupling.- 12 State estimation.- 13 Geometric theory.- 14 Solving the control problem.- 15 Effects of finite precision.- 2. Formal Orthogonal Polynomials.- 1 Definition and properties.- 2 Matrix interpretation.- 3 Adjacent families.- 4 Biorthogonal polynomials.- 5 Vector orthogonal polynomials.- 3. Padé Approximations.- 1 Preliminaries.- 2 Padé—type approximants.- 3 Padé approximants.- 4 Error estimation.- 5 Generalizations.- 6 Approximations to the exponential.- 4. Transform Inversion.- 1 Laplace transform.- 2 z—transform.- 5. Linear Algebra Issues.- 1 Singular value decomposition.- 2 Schur complement.- 3 The bordering method.- 4 Determinantal identities.- 5 Hankel matrices and related topics.- 6 Stable matrices.- 7 Recursive projection.- 6. Lanczos Tridiagonalization Process.- 1 The tridiagonalization process.- 2 The non—Hermitian Lanczos process.- 7. Systems of Linear Algebraic Equations.- 1 The method of Arnoldi.- 2 Lanczos method.- 3 Implementation of Lanczos method.- 4 Preconditioning.- 5 Transpose—free algorithms.- 6 Breakdowns.- 7 Krylov subspace methods.- 8 Hankel and Toeplitz systems.- 9 Error estimates for systems of linear equations.- 8. Regularization of Ill—Conditioned Systems.- 1 Introduction.- 2 Analysis of the regularized solutions.- 3 The symmetric positive definite case.- 4 Rational extrapolation procedures.- 9. Sylvester and Riccati Equations.- 1 Sylvester equation.- 2 Riccati equation.- 10. Topics on Nonlinear Differential Equations.- 1 Integrable systems.- 2 Connection to convergenceacceleration.- 11. Appendix: The Mathematics of Model Reduction.- 1 Model reduction by projection.- 2 Matrix interpretation.- 3 Increasing the dimension.- 4 Construction of the projection.- 5 Transfer function matrices.