376.060 Control systems 2
This course is in all assigned curricula part of the STEOP.
This course is in at least 1 assigned curriculum part of the STEOP.

2020S, VO, 3.0h, 4.5EC


  • Semester hours: 3.0
  • Credits: 4.5
  • Type: VO Lecture

Learning outcomes

After successful completion of the course, students are able to

  • understand and apply the mathematical principles and methods to describe and analyze nonlinear systems.
  • apply Lyapunov theory to analyze stability and devise nonlinear control strategies such as integrator backstepping, PD control and computed torque.
  • utilize singular perturbation methods to reduced-order models systematically.
  • develop nonlinear control schemes based on differential-geometric and differential-algebraic methods such as differential flatness or exact input-state linearization.

Subject of course

introduction to nonlinear system theory, examples of nonlinear systems (mechanical, electrical, hydraulic), stick-slip effect, basics of dynamical systems, existence and uniqueness of solutions, sensitivity equations, Lyapunov stability, invariance principle of Krasowskii-LaSalle, direct and indirect method of Lyapunov, Lyapunov equation, stability of non-autonomous systems, Lemma of Barbalat, singular perturbation theory, fast and slow manifold, boundary layer model, Theorem of Tikhonov, Lyapunov-based controller design (simple PD-law, computed torque, integrator backstepping, generalized backstepping, recursive backstepping), affine-input systems, exact input-output and input-state linearization of SISO- and MIMO-systems, relative degree, zero dynamics, trajectory tracking, flatness, basics of differential geometry (manifold, tangent and cotangent space, Lie derivatives, Theorem of Frobenius), observer design for linear time-variant systems

Teaching methods

lecture, presentation of examples during the lecture

Mode of examination


Additional information

A preliminary discussion is given in the first lecture.



Course dates

Tue08:00 - 10:0010.03.2020EI 4 Reithoffer HS KUGI
Wed08:00 - 10:0011.03.2020EI 4 Reithoffer HS KUGI

Examination modalities

oral exam

Course registration

Begin End Deregistration end
15.04.2020 08:00 15.05.2020 23:59

Registration modalities:

Die Anmeldung zur LVA ist für den online-Zugang zu TUWEL erforderlich. Die Vorlesung wird in Form von Online-Vorlesungen durchgeführt, wobei der Zugang in TUWEL zu finden ist.



Lecture notes are available here.

Preceding courses

Accompanying courses

Continuative courses