Course Information

Lectures: Tuesdays and Thursdays, 5:20 pm -- 6:55 pm, Kresge Clrm 319

Instructor:  Abhishek Halder, Dept. of Applied Mathematics and Statistics


Office hours: Fridays, 1 pm -- 2 pm, Baskin Engineering 365b


Catalog Description

Covers analysis and design of nonlinear control systems using Lyapunov theory and geometric methods. Includes properties of solutions of nonlinear systems, Lyapunov stability analysis, effects of perturbations, controllability, observability, feedback linearization, and nonlinear control design tools for stabilization. Prerequisite(s): basic knowledge of mathematical analysis and ordinary differential equations is assumed. Enrollment restricted to graduate students; undergraduates may enroll by permission of the instructor. Offered in alternate academic years.



There is no textbook for this course. Instructor's notes will be available to the students. Following is a list of excellent reference books (none of which will be followed exactly). These books have different styles, focus and varying levels of difficulty depending on readers' mathematical background.

1. Hassan K. Khalil, Nonlinear Systems. Pearson, 3rd edition, 2001.

2. Mathukumalli Vidyasagar, Nonlinear Systems Analysis. Classics in Applied Mathematics, No. 42, SIAM, 2nd edition, 2002.

3. Alberto Isidori, Nonlinear Control Systems. Springer (Communications and Control Engineering), 3rd edition, 1995.

4. Alberto Isidori, Nonlinear Control Systems II. Springer (Communications and Control Engineering), 1999.

5. Andrei Agrachev and Yuri Sachkov, Control Theory from the Geometric Viewpoint. Encyclopaedia of Mathematical Sciences (Book 87), Springer, 2004.

6. Eduardo D. Sontag, Mathematical Control Theory: Deterministic Finite-Dimensional Systems, Springer, 2nd edition, 1998.



60% from Homework: There will be 6 homeworks. Tentatively homeworks will be assigned on Tuesday or Thursday nights, and will be due in a week (on next Tuesday or Thursday in class). Submitting the homework late by a day will result 30% penalty on the actual score for that homework. This means 60% penalty for 2 days late, etc. So more than 3 days late submission will receive no credit.

The homeworks will involve analytical and computational problem solving. Students are encouraged to collaborate and discuss the homeworks, but need to write down the solution and codes on their own.

40% from Take Home FinalA take home final test will be posted on March 15 (Thursday) and will be due (submit as e-mail attachment to instructor OR submit in person in the instructor's office) no later than March 22 (Thursday).


Students with Disabilities

UC Santa Cruz is committed to creating an academic environment that supports its diverse student body. If you are a student with a disability who requires accommodations to achieve equal access in this course, please submit your Accommodation Authorization Letter from the Disability Resource Center (DRC) to me privately during my office hours or by appointment, preferably within the first two weeks of the quarter. At this time, I would also like us to discuss ways we can ensure your full participation in the course. I encourage all students who may benefit from learning more about DRC services to contact DRC by phone at 831-459-2089, or by email at