MAE 281A - Nonlinear Systems (Winter 2020)

Department of MAE, UCSD


Course web address:

Instructor: Prof. Miroslav Krstic, 1808 EBUI,

Teaching Assistant: Cenk Demir (, Imoleayo Abel (, Drew Steeves ( 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 pm (2101 EBUI)

Wednesdays   11:00 am (2101 EBUI)

Fridays             1:00 pm (2101 EBUI)


Final Exam: Due Thursday, March 19, 11:00 am - 2101 EBU1


Final (with solutions)


Grading: Homework 30% and Final 70%

Homework (pdf)

Previous Final Practice (pdf)

Homework Solutions:

Homework 1

Homework 2

Homework 4

Homework 5

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. 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. Center manifold theorem.