CDS 240, Spring 2016

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Nonlinear Dynamical Systems


  • Richard Murray (CDS/BE),
  • John Doyle (CDS),
  • Lectures: MWF, 2-3 pm, 314 ANB
  • Office hours: by appointment

Teaching Assistant

  • TBD
  • Contact:
  • Office hours: TBD

Course Description

CDS 240. Nonlinear Dynamical Systems. 9 units (3-0-6); third term. Prerequisites: CDS 140. Analysis of nonlinear dynamical systems modeled using differential equations, including invariant and center manifolds, bifurcations, limit cycles, regular and singular perturbations, the method of averaging, input/output stability. Additional advanced topics may be included based on student and instructor interests. Instructors: Doyle, Murray.

Lecture Schedule

Week Date Topic Suggested Reading/Lecture Notes Homework
1 28 Mar
30 Mar
Stability of perturbed systems
  • Vanishing perturbations
  • Non-vanishing perturbations
  • Slowiy varying systems
HW #1
Due 11 Apr
3 1 Apr
6 Apr
Perturbation theory
  • Periodic perturbations
  • Averaging
  • Singular Perturbations
3 11 Apr
13 Apr
15 Apr
Interconnected Systems
  • Input/output stability
  • Small gain theorem
  • Passivity
  • Absolute stability, circle criterion, Popov criterion
  • Describing functions
HW #2
Due 25 Apr
4 18 Apr
20 Apr
22 Apr
25 Apr
5 27 Apr
29 Apr
Lagrangian and Hamiltonian systems
  • Lagrangian mechanics
  • Lagrange-d'Alembert equations
  • Conservation laws
  • Hamiltonian systems
  • Stability properties
HW #3
Due 9 May
6 4 May
6 May
7 9 May
11 May
Nonnormal systems See dropbox folder HW #4
Due 25 May
8 13 May
16 May
9 23 May
25 May


Course Textbooks

  • H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893
  • S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536
  • F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346

Additional Sources:

  • L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164
  • S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777


Collaboration Policy

Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reflect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed.

Grading Policy

The final grades will be evaluated based on homework assignments.