MTM5101 – Dynamical Systems and Chaos (Fall 2023-2024)
Instructor Information
General Information
Schedule: Friday, 09:00-12:00
Classroom: KMB-306
Office Hours: Friday, 14:00-17:00 (and/or by appointment)
Expectations and Goals
Course Materials
Acknowledgement
Course Schedule
Week 1 (06.10.2023): System Dynamics and State Space Representation, Measurement Outputs, Modern Challenges in Dynamical Systems, Some of the Uses of Models
[Slide]
Week 2 (13.10.2023): Linear vs Nonlinear Systems: Examples of Nonlinear Systems, Superposition Principle, Invariant Sets
[Slide]
Week 3 (20.10.2023): Common Nonlinear Phenomena, Fundamental Properties: Existence and Uniqueness
[Slide]
Week 4 (27.10.2023): Fundamental Properties: Existence and Uniqueness, Second Order Time-Invariant Systems: Phase Portraits and Local Analysis
[Slide]
Week 5 (03.11.2023): Second Order Time-Invariant Systems: Local Analysis and Existence of Periodic Orbits
[Slide]
Week 6 (10.11.2023): Stability Definitions and Solution Characteristics, Lyapunov Stability Analysis: Lyapunov’s Indirect Method, System Energy and “Energy-Like" Functions
[Slide]
Week 7 (17.11.2023): Lyapunov Functions and Lyapunov’s Stability Theorem
[Slide]
Week 8 (24.11.2023): Lyapunov Theorems for GAS, GES
[Slide]
Week 9 (01.12.2023): Midterm Exam
[Midterm Exam of Fall 2022-2023]
Results are announced in obs.yildiz.edu.tr!
Week 10 (08.12.2023): Alternative Lyapunov Theorem for GAS with Comparison Functions, Systems with Inputs: ISS, iISS, Strong iISS Systems, Lyapunov Characterizations, Cascade Systems
[Slide]
* Week 11 (15.12.2023): Time-Delay Systems (TDS): Notations, GAS, ISS, iISS, LKF Characterizations, Soln Characterizations, Robustness Properties
[Slide]
* Week 12 (22.12.2023): Cascade Interconnected iISS TDS
[Slide]
Week 13 (29.12.2023): Research Seminar
Week 14 (05.01.2024): Student Presentations Workshop
* The content of these weeks will not be covered in the final exam!
Course Evaluation
Midterm: 30 %
Presentation: 15 %
Project Report: 15 %
Final: 40 %
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