invariance-like theorems (advanced stability analysis)

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Nonlinear Systems Analysis Lecture Note Section 8.3 Invariance-like Theorems (Advanced Stability Analysis) Feng-Li Lian NTU-EE Sep05 – Jan06 NTUEE-NSA-Ch8.3-2 Feng-Li Lian © 2005 Outline The Center Manifold Theorem (8.1) Region of Attraction (8.2) Invariance-Like Theorems (8.3) Stability of Periodic Systems (8.4)

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Page 1: Invariance-like Theorems (Advanced Stability Analysis)

Nonlinear Systems Analysis

Lecture Note

Section 8.3

Invariance-like Theorems(Advanced Stability Analysis)

Feng-Li LianNTU-EE

Sep05 – Jan06

NTUEE-NSA-Ch8.3-2Feng-Li Lian © 2005Outline

The Center Manifold Theorem (8.1)Region of Attraction (8.2)Invariance-Like Theorems (8.3)Stability of Periodic Systems (8.4)

Page 2: Invariance-like Theorems (Advanced Stability Analysis)

NTUEE-NSA-Ch8.3-3Feng-Li Lian © 2005Invariance-like Theorems (8.3)

NTUEE-NSA-Ch8.3-4Feng-Li Lian © 2005Barbalat’s Lemma

Page 3: Invariance-like Theorems (Advanced Stability Analysis)

NTUEE-NSA-Ch8.3-5Feng-Li Lian © 2005Barbalat’s Lemma

NTUEE-NSA-Ch8.3-6Feng-Li Lian © 2005Barbalat’s Lemma

Page 4: Invariance-like Theorems (Advanced Stability Analysis)

NTUEE-NSA-Ch8.3-7Feng-Li Lian © 2005Theorem 8.4

NTUEE-NSA-Ch8.3-8Feng-Li Lian © 2005Theorem 8.4

Page 5: Invariance-like Theorems (Advanced Stability Analysis)

NTUEE-NSA-Ch8.3-9Feng-Li Lian © 2005Theorem 8.4

NTUEE-NSA-Ch8.3-10Feng-Li Lian © 2005Theorem 8.4: Part of Proof

Page 6: Invariance-like Theorems (Advanced Stability Analysis)

NTUEE-NSA-Ch8.3-11Feng-Li Lian © 2005Theorem 8.4: Part of Proof

NTUEE-NSA-Ch8.3-12Feng-Li Lian © 2005Theorem 8.5: U.A.S.

Page 7: Invariance-like Theorems (Advanced Stability Analysis)

NTUEE-NSA-Ch8.3-13Feng-Li Lian © 2005Theorem 8.5: U.A.S.

NTUEE-NSA-Ch8.3-14Feng-Li Lian © 2005Theorem 8.5: U.A.S.

Page 8: Invariance-like Theorems (Advanced Stability Analysis)

NTUEE-NSA-Ch8.3-15Feng-Li Lian © 2005Example 8.11: L.T.V.

NTUEE-NSA-Ch8.3-16Feng-Li Lian © 2005Example 8.11: L.T.V.

Page 9: Invariance-like Theorems (Advanced Stability Analysis)

NTUEE-NSA-Ch8.3-17Feng-Li Lian © 2005Example 8.11: L.T.V.

NTUEE-NSA-Ch8.3-18Feng-Li Lian © 2005Example 8.12: Adaptive Control

Page 10: Invariance-like Theorems (Advanced Stability Analysis)

NTUEE-NSA-Ch8.3-19Feng-Li Lian © 2005Example 8.12: Adaptive Control

NTUEE-NSA-Ch8.3-20Feng-Li Lian © 2005Example 8.12: Adaptive Control

Page 11: Invariance-like Theorems (Advanced Stability Analysis)

NTUEE-NSA-Ch8.3-21Feng-Li Lian © 2005Example 8.12: Adaptive Control

NTUEE-NSA-Ch8.3-22Feng-Li Lian © 2005Example 8.12: Adaptive Control

Page 12: Invariance-like Theorems (Advanced Stability Analysis)

NTUEE-NSA-Ch8.3-23Feng-Li Lian © 2005Example 8.12: Adaptive Control

NTUEE-NSA-Ch8.3-24Feng-Li Lian © 2005Example 8.12: Adaptive Control

Page 13: Invariance-like Theorems (Advanced Stability Analysis)

NTUEE-NSA-Ch8.3-25Feng-Li Lian © 2005Example 8.12: Adaptive Control

NTUEE-NSA-Ch8.3-26Feng-Li Lian © 2005Example 8.12: Adaptive Control

Page 14: Invariance-like Theorems (Advanced Stability Analysis)

NTUEE-NSA-Ch8.3-27Feng-Li Lian © 2005Observability of Time-Varying Systems

NTUEE-NSA-Ch8.3-28Feng-Li Lian © 2005Observability of Time-Varying Systems

Page 15: Invariance-like Theorems (Advanced Stability Analysis)

NTUEE-NSA-Ch8.3-29Feng-Li Lian © 2005Observability of Time-Varying Systems

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