CONTENTS
PREFACE xi
1 INTRODUCTION, MOTIVATION AND
GEOMETRIC TOOLS 1
1.1 Models of systems and system identification 1
1.2 A new generation of system identification algorithms 6
1.2.1 State space models are good engineering models 6
1.2.2 How do subspace identification algorithms work ? 9
1.2.3 What’s new in subspace identification ? 11
1.2.4 Some historical elements 12
1.3 Overview 15
1.4 Geometric tools 19
1.4.1 Orthogonal projections 19
1.4.2 Oblique projections 21
1.4.3 Principal angles and directions 23
1.4.4 Statistical tools 25
1.4.5 Geometric tools in a statistical framework 27
1.5 Conclusions 29
2 DETERMINISTIC IDENTIFICATION 31
2.1 Deterministic systems 32
2.1.1 Problem description 32
2.1.2 Notation 33
2.2 Geometric properties of deterministic systems 37
2.2.1 Matrix input-output equations 37
2.2.2 Main Theorem 37
2.2.3 Geometric interpretation 44
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