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Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems Dr. Zhiming Wang Professor of Mathematics East China Normal University, Shanghai, China Advanced ODE Course December 02, 2014

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Page 1: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems

Advanced ODE-Lecture 10

Lyapunov Stability for Linear Systems

Dr. Zhiming Wang

Professor of Mathematics

East China Normal University, Shanghai, China

Advanced ODE Course December 02, 2014

Page 2: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems

Outline

Lyapunov Stability for Linear Autonomous Systems Local Stability with Perturbation Linearization

Page 3: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems

Lyapunov Stability for Linear Autonomous Systems

Page 4: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems
Page 5: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems
Page 6: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems
Page 7: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems

Linear Autonomous System with Perturbation

Page 8: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems
Page 9: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems
Page 10: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems
Page 11: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems
Page 12: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems

Linearization

Page 13: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems
Page 14: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems
Page 15: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems
Page 16: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems
Page 17: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems
Page 18: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems
Page 19: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems
Page 20: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems
Page 21: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems
Page 22: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems

Summary

Page 23: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems

Homework

Review today’s contents of class.

Page 24: Advanced ODE-Lecture 10 Lyapunov Stability for Linear Systems

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On Lyapunov stability of scalar stochastic time-delayed ...static.springer.com/sgw/documents/1387730/application/pdf/Ehsan...On Lyapunov stability 65 Stability conditions for DDEs

Lecture 4 — Lyapunov Stability Stability: If P=PT>0, then the Lyapunov Stability Theorem implies (local=global) asymptotic stability, hence the eigenvalues of Amust satisfy Re

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