Nonlinear Control Systems

Content and learning objectives:


  • Definition of nonlinear systems
  • Description and classification of typical nonlinearities
  • Lyapunov stability

Analysis and design in state space

  • Features and construction of the phase space
  • Sliding mode

Harmonic balance

  • Derivation of the description function
  • Equation of harmonic balance
  • Two-locus-method
  • Stability behaviour of limit cycles

Direct method of Lyapunov

  • Lyapunov criteria for stability
  • Stability for linear state space models

Controller design by exact linearization

  • State transformation of nonlinear systems
  • Exact linearization by compensation
  • Partial feedback linearization
  • Zero dynamics

The objective is to impart the fundamentals of the analysis of nonlinear systems. On the basis of a classification of dynamical systems and related examples, different analysis methods for the computation of phenomena occurring in nonlinear systems will be dealt with. The stability features of such systems will be dealt with extensively. Thus, we are going to impart an understanding of the behaviour of nonlinear systems and present the mathematical aspects of dealing with these systems.

Reference for students

Regarding further information about contents and organization of our courses, please visit the central e-learning platform PAUL.