Dipartimento di Ingegneria Elettrica ed Elettronica
UniversitÓ di Cagliari, Italy

Course: Analysis and Control of Cyber-Physical Systems
Master Degree in: Electronic Engineering
Semester/Credits/Hours: Spring semester, 6 credits, 60 h
Instructor: Alessandro Giua - email: giua@unica.it
Ufficio: DIEE pad B, 3║ piano.   Tel: 070-675-5751
Web site: https://www.alessandro-giua.it/UNICA/ACCPS


Midterm 2024: Friday 19 April, Room I_IB - ex Aula BA

Final test 2024: to be arranged


Texbook: A. Giua. Notes for the course Analysis and Control of Cyber-Physical Systems, 18 February 2022. The material in Chapter 14 and Appendices C and D is not currently part of the syllabus.

Schedule 2024 :
Tuesdays15:00-17:00 h Room: G_TA - ex Aula Mocci
Thursdays15:00-18:00 hRoom: I_1D - ex Aula M
Extra classes:

  1. Monday March 12, 12:00-14:00, Room: B_TB - ex Aula B
  2. Monday March 18, 12:00-14:00, Room: I_1A - ex Aula P
  3. Tuesday April 9, 17:00-18:00, Room: G_TA - ex Aula Mocci
  4. Tuesday April 16, 17:00-18:00, Room: G_TA - ex Aula Mocci
  5. Monday April 22, 12:00-14:00, Room: I_1A - ex Aula P

Office hours: By appointment, in person or via Teams. Preferably Wed 11:00-13:00.

Channel Teams: ACCPS 2024

Tutor: Tianyu LIU (tianyuliu0401@gmail.com). On Teams: t.liu@studenti.unica.it


The course provides an introduction to cyber-physical systems (CPSs), i.e., dynamical systems composed by logical components (driven by event occurrences) interacting with physical components (described by time-driven models). From a control systems perspective CPSs are hybrid systems, combining discrete event and continuous dynamics. The course is structured into two parts. The first part presents discrete event systems and supervisory control. The second part is devoted to the modeling and analysis of hybrid systems and introduces some approaches for formal modeling and verification.


  1. Classification of dynamical systems (2h lecture)
    Time-driven systems. Discrete-event systems. Hybrid systems.
  2. Automata models for discrete event systems (12h 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 (12h 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. Stability and stabilization of linear switched systems (8h lecture + 2h homework/ 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.
  6. Reachability analysis of hybrid systems (6h lecture + 2h homework)
    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.

Mid-term and final test 2024 :

Homeworks 2024:

Mid-term and final test (previous years):

Homeworks (previous years):

Other material

  • For the first part of the course (discrete event systems) you can find useful material (in Italian) on the webpage of the course [Automi e reti di Petri].
  • For the second part of the course (hybrid systems) here is a series of additional [exercises on HS].



  • All tests during regular exam sessions are oral.
  • Students attending classes are offered the additional opportunity to pass the exam taking two written tests: a mid-term and a final one. The final test can be replaced by a project.Mid-term and final test consists in a series of problems to be solved in class and may include some theoretical questions. Students cannot consult any material during the test, except for a single A4 sheet where they can summarize notes, diagrams or other reference material.
  • Scores for the written tests (or project) are as follows:
    - Mid-term written test (Part I: discrete event systems) 25 points
    - Final written test (Part II: hybrid systems) or project 25 points
    - Homework 15 points
  • The final grade G will depend on the total points (TP): G = 30 if TP ≥ 60, else G = floor(TP/2).