Lehrstuhl für Mechatronik in Maschinenbau und Fahrzeugtechnik (MEC)

Hybrid Dynamical Systems


Hybrid systems arise whenever continuous and discrete dynamics interact. This is often the case when logic decision making or embedded control actions are combined with continuous physical processes. For instance, when computers and physical processes interact. Nearly all dynamic processes in automation, logistics, production, biology, etc. display such heterogeneity. In order to capture the evolution and the interaction of discrete and continuous processes, rigorous mathematical frameworks are needed. Usually, such frameworks consist of differential equations or inclusions that describe the continuous dynamics of the hybrid process, and automata, finite-state machines or Petri nets that describe the discrete and logical behavior. The collection of analysis and synthesis methods developed for these frameworks forms the research area of hybrid systems theory, which plays an important role in the multi-disciplinary design of many technological systems. The captured dynamical patterns are thus rich and continue to stand for a front research in control theory.

Course Content

The course Hybrid Systems gives an overview of the basic concepts and modeling techniques.  Also, it aims to provide rigorous mathematical foundations of the covered methods.  The focus is conceptual rather than technical.  Applications are addressed throughout the course.

Symbolic models: Systems; Hybrid systems; Finite systems; Hybrid automata / Petrinets.

Symbolic methods: Model abstraction; Simulation; Symbolic control and verification.

Algebraic models and methods: Mixed integer models and optimal control, impulsive differential systems, switched systems, stability.


  • Cassandras, C., Lafortune, S. Introduction to Discrete Event Systems. Springer, 2008.
  • Tabuada, P. Verification and Control of Hybrid Systems. Springer, 2009.
  • Goebel, R., Sanfelice, R.G., Teel, A.R. Hybrid Dynamical Systems. Princeton University Press, 2012.


    Prof. Dr.-Ing. Naim Bajcinca
    +49 631/205-3230
    Gebäude 42, Raum 262
    Sprechstunde: nach Vereinbarung


    Iqra Batool
    +49 631/205-3702
    Gebäude 42, Raum 257
    Sprechstunde: Mittwoch, 10:00-11:00 Uhr


    V: Freitag, 13:45-15:15 Uhr
    SWS: 2V/1


    Oral examination:  30-45 min.
    Credit points:  5 ECTS


    Systems and control theory
    Algebra / Calculus
    Ordinary differential equations

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