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STABILITY ANALYSIS IN CONTINUOUS AND DISCRETE TIME PROEFSCHRIFT ter verkrijging van de graad van doctor aan de <strong>Universiteit</strong> <strong>Twente</strong>, op gezag van de rector magnificus, prof. dr. H. Brinksma volgens besluit van het College voor Promoties in het openbaar te verdedigen op vrijdag 20 januari 2012 om 14:45 uur door Nicolaas Cornelis Besseling geboren op 2 september 1979 te Hoorn
Dit proefschrift is goedgekeurd door de promotoren prof. dr. H.J. Zwart prof. dr. A.A. Stoorvogel
Page 2 and 3: Stability analysis in continuous an
Page 6: This thesis is dedicated to my pare
Page 9 and 10: Preface side(s) of the North Sea an
Page 11 and 12: Contents 5 Extension Bergman distan
Page 13 and 14: Chapter 1. Introduction This family
Page 15 and 16: Chapter 1. Introduction In this the
Page 17 and 18: Chapter 1. Introduction 600 500 400
Page 19 and 20: Chapter 1. Introduction Lemma 1.3 L
Page 21 and 22: Chapter 1. Introduction A contracti
Page 23 and 24: Chapter 1. Introduction 1.5 General
Page 25 and 26: Chapter 1. Introduction we find tha
Page 28 and 29: Chapter 2 Stability In this chapter
Page 30 and 31: is strongly stable. However its adj
Page 32 and 33: 2.1. Continuous-time case For furth
Page 34 and 35: 2.2 Discrete-time case Next, we def
Page 36 and 37: 2.2. Discrete-time case Remark 2.16
Page 38 and 39: 2.2. Discrete-time case To prove th
Page 40 and 41: 2.3. From continuous to discrete ti
Page 42 and 43: 2.3. From continuous to discrete ti
Page 44 and 45: Chapter 3 Log estimate using Lyapun
Page 46 and 47: 3.2. Estimates on operators Definit
Page 48 and 49: 3.2. Estimates on operators where w
Page 50 and 51: 3.3. Proof of Theorem 3.1 Proof: If
Page 52 and 53: Chapter 4 Bergman distance 4.1 Intr
Page 54 and 55:
4.1. Introduction � So two semigr
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4.2. Properties of semigroups with
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4.3. Properties of cogenerators wit
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4.4. Equivalence of the Bergman dis
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4.4. Equivalence of the Bergman dis
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4.5. Proof of Theorem 4.7 In partic
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4.6. Applications The first time in
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4.6. Applications In [16, Theorem I
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4.7. Conclusions stability properti
Page 73 and 74:
Chapter 5. Extension Bergman distan
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Chapter 6. Norm relations using Lag
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Chapter 7 Growth relation cogenerat
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we have for t ≥ 1 �e (A0)dt ∞
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7.1. Exponentially stable semigroup
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7.2. Bounded semigroups on a Hilber
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Substituting this in (7.11), we fin
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7.2. Bounded semigroups on a Hilber
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7.3 Conclusions 7.3. Conclusions In
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Bibliography [10] R. F. Curtain and
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Bibliography [35] M. Tucsnak and G.
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Summary of the power sequences of t
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Samenvatting machtreeksen. Dit bete
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