IV120 Continuous and Hybrid Systems

Faculty of Informatics
Spring 2019
Extent and Intensity
2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
RNDr. David Šafránek, Ph.D. (lecturer)
prof. RNDr. Jiří Barnat, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Aleš Horák, Ph.D.
Department of Machine Learning and Data Processing - Faculty of Informatics
Supplier department: Department of Machine Learning and Data Processing - Faculty of Informatics
Thu 21. 2. to Thu 16. 5. Thu 9:00–11:50 C525
Elementary mathematical knowledge: linear algebra (matrix, linear map, eigenspace), calculus (continuous function, multi-variable diferential calculus, first-order differential equations).
Elementary knowledge of computer science: finite automata, state-transition system, behavioral equivalence, bisimulation.
General knowledge of modeling and simulation: population model, feedback, simulation.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
Fields of study the course is directly associated with
Course objectives
At the end of the course students should be able to: understand elementary notions from the domain of continuous and hybrid systems;
orient themselves in methods for analysis of continuous and hybrid systems, system control and related problems;
characterize complexity of the given system;
apply computational methods to analyze dynamic properties of systems.
  • Introduction to general systems theory. System, object, model. Boulding's hierarchy. Dynamical system, causality, state transition function. Dimensionality, state equations. Feedbacks, block diagram.
  • Continuous, discrete, hybrid system. Trajectories, their existence, simulation. Examples of systems (electronics, economy, chemistry, biology).
  • System presentation - system matrix and its meaning. Non-linear systems, classes of non-linearity, linearization. Stability, characterization of stability, Lyapunov theorems. Attractors and domains of attraction. Oscillation, multi-stability, chaos. Feinberg's classification of reaction kinetics systems.
  • Reachability, reachability analysis for hybrid systems. Reachability in continuous systems - piece-wise linear systems, finite quotients.
  • Controllability. Open-loop and closed-loop control, black-box control, model-based control, controller synthesis. System observability and identifiability.
  • Parameterization, parameter uncertainty, sensitivity analysis. Tools for parameter estimation, system identification.
  • Methods for system comparison: system equivalence, bisimulation and approximative bisimulation. Robustness analysis.
  • Explained methods will be demonstrated in the form of practicals especially from the domain of computational systems biology. Tools from the following set will be employed: MATLAB/Octave, COPASI, GNA, SpaceEx/PHAVer, Ariadne.
    recommended literature
  • J.H. van Schuppen. Control and System Theory of Positive Systems, CWI Lecture notes, 2007.
  • P. Tabuada. Verification and Control of Hybrid Systems: A Symbolic Approach. Springer, 2009. xv, 202 p. ISBN 978-1-4419-0223-8.
  • VRIES, Gerda de. A course in mathematical biology : quantitative modeling with mathematical and computational methods. Philadelphia, Pa.: Society for Industrial and Applied Mathematics, 2006. xii, 309. ISBN 0898716128. info
  • LYNCH, Stephen. Dynamical systems with applications using MATLAB. Boston, Mass.: Birkhäuser, 2004. xv, 459. ISBN 3764343214. info
  • ŠTECHA, Jan and Vladimír HAVLENA. Teorie dynamických systémů : přednášky. 2. vyd. Praha: Vydavatelství ČVUT, 2002. 247 s. ISBN 8001019713. info
  • ARROWSMITH, David K. and C. M. PLACE. An introduction to dynamical systems. New York, N.Y.: Cambridge University Press, 1990. 423 s. ISBN 0521316502. info
Teaching methods
lectures, exercises
Assessment methods
50% project, 50% written exam
Language of instruction
Further Comments
Study Materials
The course is taught once in two years.
The course is also listed under the following terms Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2017, Autumn 2019.
  • Enrolment Statistics (Spring 2019, recent)
  • Permalink: https://is.muni.cz/course/fi/spring2019/IV120