School of Industrial and Information Engineering

Politecnico di Milano

Academic Year 2017/18




Maria Prandini

Dipartimento di Elettronica, Informazione e Bioingegneria
tel. 02-2399-3441 





Monday 13:30 15.15 Room L.26.01

Wednesday 10:30 13.15 Room D.0.4



Course description:

The aim of this course is to introduce the student to the area of nonlinear control systems, that is control systems characterized by the presence of a nonlinear element, which can either be the system under control or the controller itself, including sensors and actuators.

Some classical as well as modern analysis and controller design methods for nonlinear systems will be covered so as to enable the student to appreciate the diversity of phenomena that arise in nonlinear systems and to address a significant class of analysis and control design problems in a nonlinear context.


The course comprises lectures and specific sessions with numerical examples.

It is structured in two parts, the first one dealing with analysis and the second one with design.

Part 1: Analysis of nonlinear feedback systems

- absolute stability of Lure systems

- switching systems stability

- input-output stability

- passivity-based analysis

- existence and stability of periodic oscillations


Part 2: Nonlinear control design

- variable structure control

- feedback linearization

- switching control




September 18, 2017

Introduction to the course  [pdf]

Lure problem [pdf]

September 20, 2017

Lure problem [pdf]

Review of Lyapunov stability theory [pdf]

September 25, 2017

Lure problem [pdf]

Lure problem in the time varying case [pdf]

September 27, 2017

Lure problem in the time varying case [pdf]

Numerical examples on the Lure problem [pdf]

October 2, 2017

Switched systems stability and stabilization [pdf]

October 4, 2017

Input-output approach [pdf]

October 18, 2017

Input-output approach [pdf]

Input-output stability [pdf]

October 23, 2017

Passivity-based analysis [pdf]

October 30, 2017

Numerical examples on the input-output approach [pdf]

November 6, 2017

Numerical examples on passivity-based analysis [pdf]

Periodic oscillations [pdf]

November 8, 2017

Describing function method [pdf]

November 20, 2017

Numerical examples on the describing function method [pdf]

Variable structure control [pdf]



The final assessment will be a written exam consisting of both exercises and theoretical questions.



H. K. Khalil, Nonlinear Systems, Editore: Prentice-Hall

M. Vidyasagar, Nonlinear Systems Analysis, Editore: Prentice-Hall




July 20, 2017 [pdf]

June 28, 2017 [pdf]

February 9, 2017 [pdf]

September 30, 2016 [pdf]

September 14, 2016 [pdf]

February 2, 2016 [pdf]

March 3, 2016 [pdf]

June 30, 2016 [pdf]

Previous exams [in Italian]

Appello del 10 febbraio 2014 [pdf]

Appello del 28 febbraio 2014 [pdf]

Appello del 3 luglio 2014 [pdf]

Appello del 10 settembre 2014 [pdf]

Appello del 1 ottobre 2014 [pdf]