System theory (2018/2019)

Course code
Bogdan Mihai Maris
Academic sector
Language of instruction
Teaching is organised as follows:
Activity Credits Period Academic staff Timetable
Teoria 3 II semestre Diego Dall'Alba, Bogdan Mihai Maris

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Laboratorio 3 II semestre Diego Dall'Alba, Bogdan Mihai Maris

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Learning outcomes

The course objective is to give students the mathematical tools required for the analysis and modeling of linear, time-invariant (LTI) systems, and of the input/output signals to an LTI system. The model will allow students to study the main system properties and to address the general concepts of controller and filters to perform simple control actions on the dynamic system and filter operations on the input/output signals.
The mathematical tools will be based on analysis methods in the time domain, as well as of the complex variables s, z and the frequency of the input/output signals. Analysis and synthesis will be carried out both for continuous and discrete time systems and signals. The theoretical concepts acquired during the course will be consolidated with exercise sessions addressing the solution of basic problems with analytical approach and with numerical simulations.
The theoretical aspects will be integrated with MATLAB code. The LTI systems described by differential equations will be analyzed with SIMULINK tool that is integrated in the MATLAB environment.


1. Review: complex numbers, functions of complex variables, series of complex powers, convergence, Euler's formula
2. Distributions: impulse, step, ramp. Sampling and reproducibility. Sinusoidal exponential functions, time translation. Discrete signals
3. Continuous time systems. Causal LTI systems. Stability.
4. Characteristic equation of a system, elementary modes, convergence.
5. Convolution, impulsive response, forced response, BIBO stability, asymptotic stability
6. Frequency response
7. The Laplace transform. Convergence region. Properties
8. Free response and forced response in the complex plane, transfer function, zeros and poles, stability.
9. The Laplace's antitrasform, poles, residues.
10. The Fourier series for periodic signals. Frequency, pulsation, linear combination of periodic signals, synthesis equation, analysis equation. The energy and power of a signal, the discrete spectrum.
11. The Fourier transform. Conditions of existence, discontinuities.
12. Convolution and modulation. Spectrum.
13. Fourier trasform of the ideal sampling train, replication and sampling, reconstruction filters, Nyquist frequency, Shannon forumula.
14. Bode diagrams
15. Block diagrams
16. Discrete-time LTI systems. ARMA model. Impulsive response, forced response.
16. z trasform. Properties
17. The antitransformed z. Frequency response. Discrete Fourier transform

The students can integrate the reference books (Valcher for theory and Di Stefano et al. for the laboratory part) with the free text at the link:

Office hours: after class

Assessment methods and criteria

The exam is written. The students that obtain more than 27 may take an oral test, on an appointment basis.
During the course two optional intermediate written tests will be offered, that can replace, in full or partially, the written test.

Reference books
Activity Author Title Publisher Year ISBN Note
Teoria M.E. Valcher Segnali e Sistemi Ediitrice Progresso 2002
Laboratorio Di Stefano, Stubberud, Williams Regolazione Automatica Schaum -- Etas 1974
Teaching aids
Title Format (Language, Size, Publication date)
2019_04_11_Esercitazione  pdfpdf (it, 169 KB, 16/04/19)
2019_05_02_Risultati_esame_parziale  pdfpdf (it, 117 KB, 07/05/19)
2019_05_07_Correzione_esame_parziale  pdfpdf (it, 755 KB, 07/05/19)
2019_05_30_Esercitazione_Bode  pdfpdf (it, 292 KB, 31/05/19)
2019_06_12_Esami degli anni precedenti  zipzip (it, 616 KB, 12/06/19)
2019_06_24_Risultati_secondo_parziale  pdfpdf (it, 122 KB, 24/06/19)
2019_06_28_Correzione_secondo_parziale  pdfpdf (it, 1732 KB, 28/06/19)
2019_07_01_correzione_primo_appello  pdfpdf (it, 1052 KB, 03/07/19)
2019_07_15_correzione_secondo_appello  pdfpdf (it, 1340 KB, 16/07/19)
Dispensa_schemi_a_blocchi  pdfpdf (it, 124 KB, 25/04/19)
Errata_corrige_2019_04_18  pdfpdf (it, 33 KB, 19/04/19)
Esercizi_1  pdfpdf (it, 79 KB, 01/04/19)
Esercizi_2  pdfpdf (it, 876 KB, 16/04/19)
Esercizi_3  pdfpdf (it, 1199 KB, 16/04/19)
Esercizi_4  pdfpdf (it, 794 KB, 16/04/19)
Esercizi_5  pdfpdf (it, 690 KB, 16/04/19)
Esercizi_6  pdfpdf (it, 872 KB, 16/04/19)
Esercizi_7  pdfpdf (it, 491 KB, 16/04/19)
Esercizi_8  pdfpdf (it, 264 KB, 16/04/19)
Esercizi_9  pdfpdf (it, 105 KB, 25/04/19)
Secondo parziale 2012  pdfpdf (it, 386 KB, 12/06/19)
Secondo parziale 2013  pdfpdf (it, 381 KB, 12/06/19)
Soluzioni_schemi_a_blocchi  pdfpdf (it, 35 KB, 25/04/19)