### Subspace Identification for Linear Systems Theory — Implementation — Applications

The implementation of subspace identification algorithms is discussed in terms of the robust and computationally efficient RQ and singular value decompositions, which are well-established algorithms from numerical linear algebra. The algorithms are implemented in combination with a whole set of clas...

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Main Authors: , de Moor, B.L. (Author) eBook English New York, NY Springer US 1996, 1996 1st ed. 1996 Springer Book Archives -2004 - Collection details see MPG.ReNa
• 1 Introduction, Motivation and Geometric Tools
• 1.1 Models of systems and system identification
• 1.2 A new generation of system identification algorithms
• 1.3 Overview
• 1.4 Geometric tools
• 1.5 Conclusions
• 2 Deterministic Identification
• 2.1 Deterministic systems
• 2.2 Geometric properties of deterministic systems
• 2.3 Relation to other algorithms
• 2.4 Computing the system matrices
• 2.5 Conclusions
• 3 Stochastic Identification
• 3.1 Stochastic systems
• 3.2 Geometric properties of stochastic systems
• 3.3 Relation to other algorithms
• 3.4 Computing the system matrices
• 3.5 Conclusions
• 4 Combined Deterministic-Stochastic Identification
• 4.1 Combined systems
• 4.2 Geometric properties of combined systems
• 4.3 Relation to other algorithms
• 4.4 Computing the system matrices
• 4.5 Connections to the previous Chapters
• 4.6 Conclusions
• 5 State Space Bases and Model Reduction
• 5.1 Introduction
• 5.2 Notation
• 5.3 Frequency weighted balancing
• 5.4 Subspace identification and frequency weighted balancing
• 5.5 Consequences for reduced order identification
• 5.6 Example
• 5.7 Conclusions
• 6 Implementation and Applications
• 6.1 Numerical Implementation
• 6.2 Interactive System Identification
• 6.3 An Application of ISID
• 6.4 Practical examples in Matlab
• 6.5 Conclusions
• 7 Conclusions and Open Problems
• 7.1 Conclusions
• 7.2 Open problems
• A Proofs
• A.1 Proof of formula (2.16)
• A.2 Proof of Theorem 6
• A.3 Note on the special form of the Kalman filter
• A.4 Proof of Theorem 8
• A.5 Proof of Theorem 9
• A.6 Proof of Theorem 11
• A.7 Proof of Theorem 12
• A.8 Proof of Lemma 2
• A.9 Proof of Theorem 13
• A.10 Proof of Corollary 2 and 3
• A.11 Proof of Theorem 14
• B Matlab Functions
• B.1 Getting started
• B.2 Matlab Reference
• B.2.1 Directory: ‘subfun’
• B.2.2 Directory: ‘applic’
• B.2.3 Directory: ‘examples’
• B.2.4 Directory: ‘figures’
• C Notation
• References