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. Language: English