Course Description

Hybrid systems

Recent technological innovations have caused a considerable interest in the study of dynamical processes of a mixed continuous and discrete nature. Such processes are called hybrid systems and are characterized by the interaction of time-continuous models (governed by differential or difference equations) on the one hand, and logic rules and discrete-event systems (described by, e.g., automata, finite state machines, etc.) on the other.

Hybrid system appear in many practical applications, particularly in the context of cyber-physical systems, e.g. when continuous physical processes are controlled via embedded software that intrinsically has a finite number of states only (such as on/off control).

Course Objectives

This course will offer a brief overview of the field of hybrid systems ranging from modelling, over analysis and simulation, to verification and control. We will particularly focus on modelling, analysis, and control of tractable classes of hybrid systems.

Date and location

Due to the Covid-19 situation the course will be offered completely online. Final dates and times for the online lectures will be posted next to the lecture slides below together with links to the zoom meetings. The zoom meetings and recordings will be password protected and the password will be sent via email to the registered students and is available on the DISC course site.


Romain Postoyan (CRAN-CNRS) <romain.postoyan_at_univ-lorraine_dot_fr>

Manuel Mazo Jr. (TU Delft) <m.mazo_at_tudelft_dot_nl>


The course will be evaluated on the basis of three sets of homework which will be distributed through this webpage, with the indicated deadlines next to them. Submit your assignments through the DISC system.

Lecture Notes

The (old) course lecture notes can be downloaded clicking here from the DISC course intranet.

Lecture Slides

Lecture 1: Introduction
June 22, 10 am (Monday)
Lecture 2: Modelling frameworks
June 22, 11 am (Monday)
Lecture 3: Solution concept and Well-posedness
June 29, 10 am (Monday)
Lecture 4: Stability and Robustness
June 29, 11 am (Monday)
Lecture 5: Stability and Robustness
July 1, 10 am (Wednesday)
Lecture 6: Control
July 1, 11 am (Wednesday)
Lecture 7: Optimization-based control
July 6, 10 am (Monday)
Lecture 8: Formal methods and Timed Automata
July 6, 11 am (Monday)


HW1: Modelling
Deadline: September 25, 2020 (Friday)
HW2: Analysis and switched control
Deadline: October 16, 2020 (Friday)
HW3: Optimization and Formal methods
Deadline: October 23, 2020 (Friday)