Non linear system - (5 cfu)

Prof. Aurelio Piazzi Tel. 0521 905733 - Fax. 0521 905723
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The course provides concepts and some fundamental methods for the study of nonlinear dynamical continuous-time systems with special emphasis on stability theory. The presented analysis methods can be applied to a variety of physical and artificial phenomena. In the context of the automation science, some feedback systems will be analyzed also focusing on elementary synthesis procedures for nonlinear control.


Introduction: Mathematical models and nonlinear phenomena. Examples. Existence and uniqueness of the solutions of state-space nonlinear models. The comparison lemma.

Second-order systems: Qualitative behavior of linear systems. Phase diagrams. Multiple equilibria. Limit cycles. Poincaré-Bendixson criterion. Bifuracations.

Lyapunov stability theory: Autonomous systems. Lyapunov’s theorem. La Salle’s invariance principle. Linear systems and linearization. Regions of attraction. Nonautonomous systems and Lyapunov’s theorems. Linear time-varying systems and linearization. Converse theorems. Boundedness of state motions and input-to-state stability.

Frequency domain analysis of feedback systems: The describing function method. Common nonlinearities. The extended Nyquist criterion and the orbital stability of limit cycles.

Nonlinear control: The stabilization and tracking problems. The gain-scheduling approach. Lyapunov’s methods. Feedback linearization and the zero dynamics. State observers.

Attività d'esercitazione

Analysis and synthesis exercises on nonlinear systems. Simulations of state motions with SIMULINK.

Modalità d'esame

Written tests during the course lessons and final oral exam.


Sistemi multivariabili.

Testi consigliati

Lecture notes.

Testi d'approfondimento

1) H.K. Khalil – Nonlinear Systems. Third edition. Prentice-Hall, 2002.
2) J.-J. E. Slotine, W. Li – Applied Nonlinear Control. Prentice-Hall, 1991.

Ultimo aggiornamento: 13-07-2004

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