Nonlinear Control Systems (EE 60580)

University of Notre Dame


Spring 2013 - Enroll in EE60580 section 01
DeBartolo 116, TR 2:00 - 3:15
Office Hours: TBA

Description: This course uses Lyapunov methodologies to analyze and design feedback controllers for continuous-time systems modeled by systems of nonlinear differential equations. Topics include: geometric methods for planar systems, solutions to nonlinear differential equations, Lyapunov stability, computational tools using sum-of-squares programming, input-to-state stability and control Lyapunov functions, input-output stability, passivity, feedback passivation methods, feedback linearizations, normal forms, zero-dynamics, output regulation.

Course Topics

  1. Geometric Viewpoint of Dynamical Systems
  2. Solutions to Nonlinear Differential Equations
  3. Lyapunov Theory - Time-invariant Systems
  4. Lyapunov Theory - Advanced Theorems
  5. Lyapunov Theory - Time-varying Systems
  6. Input-to-State Stability (Universal Formulae)
  7. Input/Output Stability (nonlinear H-infinity)
  8. Feedback Linearization 1 (introduction - differential topology)
  9. Feedback Linearization 2 (normal form - zero dynamics - output regulation)
  10. Passivity and Feedback Passivation

Grading: 30% homework, 30% midterm, 40% final
Instructor: Michael Lemmon, Dept. of Electrical Engineering, University of Notre Dame
Textbook: H.K. Khalil, Nonlinear Systems, 3rd Edition, 2002, Prentice-Hall

Additional References:
  1. W.M. Haddad and VijaySekhar Chellaboina, Nonlinear dynamical systems and control: a Lyapunov-based approach , Princeton University Press, 2008.
  2. S. Sastry, Nonlinear systems: analysis, stability and control , Springer, 1999.
  3. R. Sepulchre, M. Jankovic, and P.V. Kokotovic, Constructive Nonlinear Control, Springer London/New York, 1997.
  4. A. Van der Schaft, L2-Gain and Passivity Techniques in Nonlinear Control, 2000, Springer-Verlag
  5. A. Isidori, Nonlinear Control Systems, 3rd Edition, 1995, Springer-Verlag
  6. A. Isidori, Nonlinear Control Systems II, 1999, Springer-Verlag
  7. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, 1990, Springer-Verlag
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