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


Classes 2021:Classes will start on March 3, 2021 via Teams.

Mid-term exam: Thursday April 16, h. 15:00, room to be assigned.


Texbook: A. Giua, Notes for the course Analysis and Control of Cyber-Physical Systems, 2020. (available on Teams)

Homework 2021:

Schedule 2021 :
Wednesdays10:00-13:15 h I_ID (ex Nuova Aula AN, Piano Ex Biblioteca)
Thursdays16:00-17:30 hon-line via Teams

Office hours: Via Microsoft Teams, by appointment (preferably Tue 11-13h).


  • Diego DEPLANO (diego.deplano@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 stability and stabilization of switched systems.


  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 + 4h 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.

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].

2020: [Hw1] [Hw2] [Hw3] [Hw4] [Hw5]


Evaluation Students attending classes are offered the option of passing the course by handing in the homework and either taking a final written test or discussing a project. All other exams are oral.