EE222
Nonlinear Systems: Analysis, Stability, and Control

• Dr. Murat Arcak, 569 Cory Hall
• arcak at berkeley.edu
• http://www.eecs.berkeley.edu/~arcak
• Office Hours: Tuesdays 3:00-4:00 pm, 569 Cory

bCourses will be used for announcements, lecture notes, assignments, grades, and solutions to tests and homework sets.

Lecture notes will be provided. The following books are recommended for reference:

• S. Sastry, Nonlinear Systems: Analysis, Stability and Control, Springer, 1999.
• H.K. Khalil, Nonlinear Systems, Prentice Hall, 3rd edition, 2002.

Homework: 30 points. Midterm: 30 points. Final: 40 points.

• Fundamental Properties of Nonlinear Systems:
  Nonlinear phenomena and examples, planar systems, bifurcations, existence and uniqueness theorems.
• Lecture 1 (PDF)
• Lecture 2 (PDF)
• Lecture 3 (PDF)
• Lecture 4 (PDF)
• Lecture 5 (PDF)
• Lecture 6 (PDF)
• Lecture 7 (PDF)
• Lyapunov Stability Theory:
  Lyapunov's direct and indirect methods. Lyapunov-based feedback stabilization examples, including backstepping and adaptive control.
• Lecture 8 (PDF)
• Lecture 9 (PDF)
• Lecture 10 (PDF)
• Lecture 11 (PDF)
• Lecture 12 (PDF)
• Lecture 13 (PDF)
• Lecture 14 (PDF)
• Robustness Analysis and Computational Methods:
  Input-to-state stability. Using level sets for reachability bounds and safety certification. Sum-of-squares techniques and semidefinite programming relaxations for stability and safety certification.
• Lecture 15 (PDF)
• Lecture 16 (PDF)
• Lecture 17 (PDF)
• Lecture 18 (PDF)
• Differential Geometric Tools for Nonlinear Control:
  Basics concepts in differential geometry, feedback linearization and design examples.
• Lecture 19 (PDF)
• Lecture 20 (PDF)
• Lecture 21 (PDF)
• Dissipative Systems:
  Definition and examples of dissipativity, application to compositional analysis of interconnected systems, case studies.
• Lecture 22 (PDF)
• Lecture 23 (PDF)
• Lecture 24 (PDF)
• Lecture 25 (PDF)