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Technical University of Munich
Technical University of Munich

Analysis and Control of Nonlinear Systems

General Information:

  •  Lecture and tutorial in English
  • 3 SWS Lecture, 2 SWS tutorial
  • 6 ECTS-Credits
  • Written closed-book exam.

This course will investigate mainly nonlinear control systems described by nonlinear differential equations and study their properties including existence, uniqueness, and continuity of their solutions and stability using different tools such as Lyapunov functions. 

 Content:

  • Fundamental Properties: existence and uniqueness of solutions, continuous dependencies on initial conditions and parameters, comparison principle;
  • Lyapunov Stability: autonomous vs non-autonomous systems, comparison functions, converse Lyapunov theorems, boundedness and ultimate boundedness, input-to-state stability, incremental stability;
  • Stability of Feedback Systems: passivity theorems, the small-gain theorems, absolute stability (circle and Popov criterion);
  • Advanced Stability Analysis: center manifold theorems, region of attraction, invariance-like theorems;
  • State Feedback Stabilization: feedback linearization, partial feedback linearization, passivity-based control, control Lyapunov functions.

Textbook:

  1. H. K. Khalil: Nonlinear Control, Prentice Hall, 2015.
  2. J.J. Slotine and W. Li: Applied Nonlinear Control, Pearson, 1991

Lecture notes and exercises:

Available at moodle.