Course Information

Zoom Lectures: Tuesdays and Thursdays, 3:20 pm -- 4:55 pm. Lecture notes and zoom videos will be available.

Instructor:  Abhishek HalderDept. of Applied Mathematics


Zoom Office Hour: Tuesdays, 9 am -- 11 am 

Remote Learning Resources for Students:

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.



70% from Homework: 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. See details at the "Homework" tab on the left menu. 

30% from Take Home FinalOf duration 24 hours. Similar in format to the HW submissions.

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