Select Academic Year:     2017/2018 2018/2019 2019/2020 2020/2021 2021/2022 2022/2023
Second Semester 
Teaching style
Lingua Insegnamento

Informazioni aggiuntive

Course Curriculum CFU Length(h)


This is an advanced course presenting a wide range of techniques for the analysis and control of cyber-physical systems. Both discrete event and hybrid models will be considered.

Dublin descriptors:
- Knowledge and understanding of cyber-pysical systems and of the formalism used to describe them.
- Applying knowledge and understanding to solve original problems concerning modeling, analysis and control of cyber-physical systems.
- Making judgements: how to manage the complexity of a cyber-physical system, selecting an appropriate mathematical model.
- Communication skills: precise description of the dynamical behavior of a cyber-physical system and of its specifications.


Competences acquired in introductory courses (laurea degree) on the analysis and control of continuous-time linear dynamical systems using input-output and state variable models


1 - Classification of dynamical systems (2h lecture)
Time-driven systems. Discrete-event systems. Hybrid systems.

2 - Automata models for discrete event systems (10h lecture + 4h homework)
Formal languages: alphabets and words, languages and operators. Deterministic finite automata: languages and properties. Nondeterministic finite automata and their languages. Equivalence between deterministic and nondeterministic automata. Fault diagnosis using automata: diagnoser, diagnosability. Modeling with automata and concurrent composition.

3 - Supervisory control of discrete event systems (6h lecture + 2h homework)
Plant, specification, supervisor and closed-loop system. Controllability and supremal controllable sublanguage. Supervisory design for language specifications. Supervisory design for state specifications.

4 - Hybrid systems and hybrid automata (8h lecture+ 2h homework + 2h lab)
State variable models of time-driven systems. Examples of hybrid systems. Autonomous hybrid automata and generalizations. Hybrid automata with inputs. Evolution of a hybrid automaton. Pathological cases of continuous and hybrid evolutions.

5 - Reachability analysis of hybrid systems (8h lecture + 2h homework + 2h lab)
State transition systems (STSs). STS associated with a hybrid automaton. Reachability of a STS. Equivalences between states of a STS. Bisimulation between states of an STS and quotient system. Classes of rectangular automata. Timed automata: regions, equivalence between states and region graph. Initialized rectangular automata and reduction to timed automata. Elements of model checking.

6 - Stability and stabilization of linear switched systems (8h lecture + 2h homeworks + 2h lab)
Elements of stability for linear and time invariants systems. Direct method of Lyapunov. Quadratic forms and singular values. Stability analysis of switched systems by common Lyapunov function. Quadratic Stabilization Stabilization by slow switching.

Teaching Methods

The course includes theoretical lectures (42h) and exercise sessions (18h). Exercises assigned to students shall be solved in class or in the lab under the instructor’s supervision and later discussed in class.

Verification of learning

All exams are oral.

Students attending classes are also offered the additional option of passing the exam taking a mid-term and a final written test.


A. Giua, Notes for the course Analysis and Control of Cyber-Physical Systems. In preparation, 2019.

More Information

The course website collects useful material to prepare the exam and further explore topics of interest.

Questionnaire and social

Share on:
Impostazioni cookie