MTM5135 – Nonlinear Dynamical Systems (Fall 2025-2026)

Instructor Information

• Instructor: Gökhan Göksu

• E-mail: gokhan [dot] goksu [at] yildiz [dot] edu [dot] tr

• Course Web Site: gokhangoksu.github.io/MTM5135

General Information

• Schedule: Wednesday, 13:00-16:00

• Classroom: KMB-228

• Office Hours: Wednesday, 09:00-12:00

Expectations and Goals

• To understand the nature and to analyze the behavior of dynamical systems and to be able to apply these ideas to special systems. The aim is to teach students to apply these concepts to real-life systems they may encounter in the future.

Course Materials

• Textbook:

  • H. K. Khalil (2002). Nonlinear Systems, Third Edition, Prentice Hall.

• Additional Reference:

  • E. D. Sontag (2004). Input to State Stability: Basic Concepts and Results, Nonlinear and Optimal Control Theory: Lectures given at the CIME summer school held in Cetraro, Italy, June 19–29, 2004, pp.163-220.

• Recommended Video Lectures by Prof. Kristin Ytterstad Pettersen:

  • [Link]

Acknowledgement

• Special thanks to Özge Kara and Gunel Hasanova for the preparation of the course scripts.

Tentative Course Schedule

• Week 1 (01.10.2025): System Dynamics and State Space Representation, Measurement Outputs, Modern Challenges in Dynamical Systems, Some of the Uses of Models
  [Slide]

• Week 2 (08.10.2025): Linear vs Nonlinear Systems: Examples of Nonlinear Systems, Superposition Principle, Invariant Sets
  [Slide]

• Week 3 (15.10.2025): Common Nonlinear Phenomena, Fundamental Properties: Existence and Uniqueness
  [Slide]

• Week 4 (22.10.2025): Fundamental Properties: Existence and Uniqueness, Second Order Time-Invariant Systems: Phase Portraits and Local Analysis
  [Slide]

• Week 5 (29.10.2025): No Class (Republic Day)
  [No Class]

• Week 6 (05.11.2025): Second Order Time-Invariant Systems: Local Analysis and Existence of Periodic Orbits
  [Slide]

• Week 7 (12.11.2025): Stability Definitions and Solution Characteristics, Lyapunov Stability Analysis: Lyapunov’s Indirect Method, System Energy and “Energy-Like" Functions
  [Slide]

• Week 8 (19.11.2025): Lyapunov Functions and Lyapunov’s Stability Theorem
  [Slide]

• Week 9 (26.11.2025): Midterm Exam
  [Midterm]

• Week 10 (03.12.2025): Lyapunov Theorems for GAS, GES
  [Slide]

• Week 11 (10.12.2025): Alternative Lyapunov Theorem for GAS with Comparison Functions, Systems with Inputs: ISS, iISS, Strong iISS Systems
  [Slide]

• Week 12 (17.12.2025): Lyapunov Characterizations of ISS/iISS/Strong iISS, Cascade Systems
  [Slide]

• Week 13 (24.12.2025): TBA
  [Slide]

• Week 14 (31.12.2025): No Class (New Year's Eve)
  [Slide]

• Week 15 (07.01.2026): Student Presentations Workshop
  [Slide]

Course Evaluation

• Midterm: 30 %

• Presentation: 15 %

• Project Report: 15 %

• Final: 40 %