서울대학교 대학원 강의 (우리말 강의)
2023년 개설된 내용입니다.
심형보 교수
This course is to introduce fundamental concepts and techniques to deal with nonlinear dynamical systems, mostly for analyzing them in view of stability. Basic concepts such as Lyapunov stability, input-output stability, passivity are introduced. Some advanced tools such as center manifold theory, averaging, and singular perturbation are also discussed.
Textbook
Khalil, Nonlinear Systems, 3rd Edition, Prentice Hall, 2002.
Textbook homepage: http://www.egr.msu.edu/~khalil/NonlinearSystems
Reference
S. Sastry, Nonlinear Systems, Springer, 1999.
J.E. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall, 1991.
M. Vidyasagar, Nonlinear Systems Analysis, Prentice Hall, 1993.
1강. (Chapter 1) Description of Nonlinear Systems, Phase Portrait and Numerical Integration
https://www.youtube.com/watch?v=gElrE8A2dl0
2강. Comparison between Linear and Nonlinear Systems
https://www.youtube.com/watch?v=NuPzZOKDrOM
3강. (Chapter 2) Behavior of Linear Systems, Behavior of Nonlinear Systems near Equilibrium, Bifurcation, Existence of Periodic Orbits
https://www.youtube.com/watch?v=zI8_z9RwzDE
4강. Matlab/Simulink, (Chapter 3) Existence and Uniqueness of Solutions (1/2)
https://www.youtube.com/watch?v=mCqSr6qtTPk
5강. Existence and Uniqueness of Solutions (2/2), Gronwall-Bellman Inequality, Continuous Dependence on Initial Condition and Parameters (1/2)
https://www.youtube.com/watch?v=518ir6EXIEg
6강. Continuous Dependence on Initial Condition and Parameters (2/2), Sensitivity Analysis, Comparison Lemma
https://www.youtube.com/watch?v=xRrzBaMqhcU
7강. (Chapter 4) Definitions regarding Stability, Definitions for Lyapunov Theorem, Local Lyapunov Stability Theorem
https://www.youtube.com/watch?v=rY4fHZHHuyA
8강. Global Lyapunov Stability Theorem, Instability Theorem, Invariance Principle (Terminology)
https://www.youtube.com/watch?v=HIJh715vFRA
9강. Invariance Principle, Stability by Linearization
https://www.youtube.com/watch?v=12imPUlV590
10강. Determining Stability by Linearization, Class K and KL Functions, Construction of Class KL Function, Lyapunov Analysis using Class K and KL Functions
https://www.youtube.com/watch?v=QQwId7PXy5A
11강. Stability of Time-varying Systems, Stability Theorem for Time-varying Systems, Linear Time-varying Systems and Linearization
https://www.youtube.com/watch?v=XCMHVwcC79Y
12강. Converse Lyapunov Theorems, Ultimate Boundedness
https://www.youtube.com/watch?v=mAtAMziaLak
13강. Input-to-State Stability, (Chapter 5) Basic Definitions, Definition of L Stability
https://www.youtube.com/watch?v=ysu2onp_j6U
14강. L Stability of State Space Model, L2 Gain for LTI Systems, L2 Stability of Nonlinear Systems
https://www.youtube.com/watch?v=B7JwG1qeorw
15강. Small-signal L2 Stability of Nonlinear Systems, Small Gain Theorem
https://www.youtube.com/watch?v=WxUZR-MFXIE
16강. (Chapter 6) Passivity of Static Map, Sector Condition, Passivity for Dynamic Systems
https://www.youtube.com/watch?v=HROBqmnZuqs
17강. Positive Real Transfer Functions, Positive Real Lemma and KYP Lemma, Passivity and Stability (1/2)
https://www.youtube.com/watch?v=Y14Te4hGZYc
18강. Passivity and Stability (2/2), Feedback and Passivity Theorem, Stability of Feedback System via Passivity, Loop Transformation
https://www.youtube.com/watch?v=15-eann-m_o
19강. (Chapter 7) Absolute Stability and Aizerman Conjecture, Circle Criterion, Graphical Interpretation of Circle Criterion
https://www.youtube.com/watch?v=Ohhe_Sq-I8U
20강. (Chapter 8) Center Manifold Theory
https://www.youtube.com/watch?v=I0q0TetLXEM
21강. Region of Attraction, Uniform Continuity of Functions, Barbalat's Lemma, Other Stability Theorems
https://www.youtube.com/watch?v=z3GzS9d4BHY
22강. Stability of Periodic Solutions, (Chapter 9) Vanishing Perturbation, Nonvanishing Perturbation
https://www.youtube.com/watch?v=YSiw4V7INj0
23강. Comparison Method, Continuity of Solutions on Infinite Time Interval, Stability of Interconnected Systems, Slowly Varying Systems
https://www.youtube.com/watch?v=rB2nDtZZhCA
24강. (Chapter 10) Averaging Theory
https://www.youtube.com/watch?v=4Fv7jWbWWng
25강. (Chapter 11) Standard Singular Perturbation Model, Time Scale Separation Property
https://www.youtube.com/watch?v=XBZWFUhqHTY
26강. Slow Manifold, Stability Analysis using Singular Perturbation
https://www.youtube.com/watch?v=hTiIiKxG_oM