Nonlinear Systems Analysis
Lecture Note 16
Section 4.8
(Ultimate) Boundedness(Lyapunov Stability)
Feng-Li LianNTU-EE
Sep05 – Jan06
NTUEE-NSA-Ch4.7-2Feng-Li Lian © 2005Outline
Introduction (L9)
Autonomous Systems (4.1 L9)
• Basic stability definitions
• Lyapunov’s stability theorems
• Variable gradient method
• Region of attraction
• Instability
The Invariance Principle (4.2, L10)
• LaSalle’s theorem
Linear Systems and Linearization (4.3, L11)
Comparison Functions (4.4, L12)
Non-autonomous Systems (4.5, L13)
Linear Time-Varying Systems & Linearization (4.6, L14)
Converse Theorems (4.7, L15)
Boundedness & Ultimate Boundedness (4.8, L16)
Input-to-State Stability (4.9, L17)
NTUEE-NSA-Ch4.7-3Feng-Li Lian © 2005(Ultimate) Boundedness
NTUEE-NSA-Ch4.7-4Feng-Li Lian © 2005(Ultimate) Boundedness
NTUEE-NSA-Ch4.7-5Feng-Li Lian © 2005(Ultimate) Boundedness
NTUEE-NSA-Ch4.7-6Feng-Li Lian © 2005(Ultimate) Boundedness
NTUEE-NSA-Ch4.7-7Feng-Li Lian © 2005via Lyapunov Analysis
NTUEE-NSA-Ch4.7-8Feng-Li Lian © 2005via Lyapunov Analysis
NTUEE-NSA-Ch4.7-9Feng-Li Lian © 2005via Lyapunov Analysis
NTUEE-NSA-Ch4.7-10Feng-Li Lian © 2005via Lyapunov Analysis
NTUEE-NSA-Ch4.7-11Feng-Li Lian © 2005via Lyapunov Analysis
NTUEE-NSA-Ch4.7-12Feng-Li Lian © 2005Definitions of UB, GUB, UUB, GUUB
NTUEE-NSA-Ch4.7-13Feng-Li Lian © 2005Definitions of UB, GUB, UUB, GUUB
NTUEE-NSA-Ch4.7-14Feng-Li Lian © 2005Definitions of UB, GUB, UUB, GUUB
NTUEE-NSA-Ch4.7-15Feng-Li Lian © 2005Lyapunov Analysis - 1
NTUEE-NSA-Ch4.7-16Feng-Li Lian © 2005Lyapunov Analysis - 2
NTUEE-NSA-Ch4.7-17Feng-Li Lian © 2005Lyapunov Analysis - 3
NTUEE-NSA-Ch4.7-18Feng-Li Lian © 2005Lyapunov Analysis - 4
NTUEE-NSA-Ch4.7-19Feng-Li Lian © 2005Lyapunov Analysis - 5
NTUEE-NSA-Ch4.7-20Feng-Li Lian © 2005Lyapunov Analysis - 6
NTUEE-NSA-Ch4.7-21Feng-Li Lian © 2005Lyapunov Analysis - 7
NTUEE-NSA-Ch4.7-22Feng-Li Lian © 2005Lyapunov Analysis - 8
NTUEE-NSA-Ch4.7-23Feng-Li Lian © 2005Lyapunov Analysis - 9
NTUEE-NSA-Ch4.7-24Feng-Li Lian © 2005Lyapunov Analysis - 10
NTUEE-NSA-Ch4.7-25Feng-Li Lian © 2005Lyapunov Analysis - 11
NTUEE-NSA-Ch4.7-26Feng-Li Lian © 2005Theorem 4.18: G.U.U.B.
NTUEE-NSA-Ch4.7-27Feng-Li Lian © 2005Theorem 4.18: G.U.U.B.
NTUEE-NSA-Ch4.7-28Feng-Li Lian © 2005Theorem 4.18: G.U.U.B.
NTUEE-NSA-Ch4.7-29Feng-Li Lian © 2005Theorem 4.18: G.U.U.B.
NTUEE-NSA-Ch4.7-30Feng-Li Lian © 2005Theorem 4.18: G.U.U.B.
NTUEE-NSA-Ch4.7-31Feng-Li Lian © 2005Example 4.24
NTUEE-NSA-Ch4.7-32Feng-Li Lian © 2005Example 4.24
NTUEE-NSA-Ch4.7-33Feng-Li Lian © 2005Example 4.24
NTUEE-NSA-Ch4.7-34Feng-Li Lian © 2005Example 4.24
NTUEE-NSA-Ch4.7-35Feng-Li Lian © 2005Example 4.24
NTUEE-NSA-Ch4.7-36Feng-Li Lian © 2005Example 4.24
NTUEE-NSA-Ch4.7-37Feng-Li Lian © 2005Example 4.24
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