MAE 281A - Nonlinear Systems (Winter 2019)

Department of MAE, UCSD


Course web address:

Instructor: Prof. Miroslav Krstic, 1808 EBUI,

Teaching Assistant: Huan Yu ( and Mostafa Bagheri (, 2101 EBUI


      Khalil, Nonlinear Systems, Prentice Hall, 2001.

      (supplemental) Krstic, Kanellakopoulos, and Kokotovic, Nonlinear and Adaptive Control Design, Wiley, 1995.

Prerequisites: Linear Systems (MAE 280A) or consent of instructor


Time and Place: TuTh, 8:00-9:20 am, PCYNH (Pepper Canyon Hall) 120

Cancelled classes: TBD  

Make up classes: TBD


Office Hours by Instructor: Mondays 10:00-11:00 am (1808 EBUI)

Office Hours by TA:

Mondays         1:00-2:00 pm (2101 EBUI)

Wednesdays   1:00-2:00 pm (2101 EBUI)

Fridays             1:00-2:00 pm (2101 EBUI)


Final Exam: Due Thursday, March 21, 11:00 am - 2101 EBU1



Grading: Homework 30% and Final 70%

Homework (pdf)

Previous Final Practice (pdf)

Homework Solutions:

Homework 1

Homework 2

Homework 4

Homework 6

Homework 8

Homework 10


Course Objective: The course will give the students an in-depth introduction to stability and other analysis techniques for nonlinear systems and prepare them for courses on nonlinear control design (MAE 281B) and adaptive control (MAE 282, alternate years). Students from all departments are welcome.


Topics: Existence and uniqueness of solutions of ODEs, sensitivity equations. Stability, direct and converse Lyapunov theorems, LaSalle's theorem, linearization, invariance theorems. Center manifold theorem. Stability of perturbed systems with vanishing and non-vanishing perturbations, input-to-state ability, comparison method. Input-output stability. Perturbation theory and averaging. Singular perturbations. Circle and Popov criteria.