IMT School for Advanced Studies Lucca

General information

Course title: Identification, Analysis and Control of Dynamical Systems (ATCS)
Instructor: A. Bemporad
Duration: 20 hours
January 2017
Version: Last updated on January 29, 2017.


The course provides an introduction to dynamical systems, with emphasis on linear systems. After introducing the basic concepts of stability, controllability and observability, the course covers the main techniques for the synthesis of stabilizing controllers (state-feedback controllers and linear quadratic regulators) and of state estimators (Luenberger observer and Kalman filter).

The course also covers data-driven approaches of parametric identification (least-squares, intrumental variables, subspace and prediction error methods) to obtain models of dynamical systems from a set of data, with emphasis on the analysis of the robustness of the estimated models w.r.t. noise on data and on the numerical implementation of the algorithms.

Course topics

Introduction to dynamical systems

  • Equilibrium points and stability
  • Linearization of nonlinear systems
  • Discretization of continous-time systems
  • Transfer functions
  • Observability and controllability of LTI systems
  • Luenberger's observer and state-feedback controllers
  • Linear Quadratic Regulator and Kalman filter
  • Basic concepts on Linear Parameter-Varying systems

System identification

  • Least-squares methods and recursive identification
  • Intrumental-variables methods
  • Consistent and unbiased estimators
  • Prediction error methods


Linear algebra; Basic concepts of statistics.

Grading plan

Students will be evaluated by preparing and giving a presentation after the end of the course. They may present a project of their own related to the topics discussed during the course, or present a research article.

Suggested readings

We recommend the following bibliographic resources:

System identification

  1. L. Ljung, System identification: theory for the user, Prentice-Hall Englewood Cliffs, NJ, 1999.
  2. T. Soderstrom and P. Stoica, System identification, Prentice Hall International, 1989. Available online.
  3. P. Van Overschee, B. De Moor, Subspace Identification for Linear Systems, Theory, Implementation, Applications , Kluwer Academic Publishers, 1996. Available online.
  4. L. Ljung, Perspectives on system identification, Annual Reviews in Control, Vol. 34, No. 1, pp. 1-12, 2010.

Course material

  1. Dynamical systems: analysis and control (slides)
  2. Systems Identification (slides) (matlab)