MAE 281A - Nonlinear Systems (Winter 2017)

Department of MAE, UCSD


Course web address:

Instructor: Prof. Miroslav Krstic, 1808 EBUI, 822-1374,

Teaching Assistant: Stephen Chen and Shumon Koga, 2101 EBUI, and


      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, WLH 2207

Cancelled classes:TBD  

Make up classes:TBD


Office Hours by Instructor : Mondays, 9-10 am, 1808 EBU1

Office Hours by TA: Mondays and Fridays, 1-2 pm, 2101 EBU1

Final Exam: Thursday, March 23, 8:00-11:00


Homework (pdf) 30%

Final 70%


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.


Homework Solutions:

HW #1

HW #2

HW #3

HW #4

HW #5

HW #6

HW #8

HW #9

HW #10