Academic Year 2023-2024



Franco Blanchini
Unit Credits
Teaching Period
First Period
Course Type
Prerequisites. Prerequisites:

Basic calculus notions, integrals and differential calculus in several variables. Basic notions of linear algebra: matrices, rank, kernel, range, determinants, eigenvalues and eigenvectors.

Basic notions on complex numbers. Fourier series and Laplace transform. Basic notions of physics: fundamental lows of mechanics, fluid dynamics, heat transfer, electromagnetism, electrical circuits. Notions of probability. Basics of software implementation.

Mandatory prerequisites: none.

Teaching Methods. – Class lectures

– Class exercises

– Virtual visit to the laboratory

Verification of Learning. To check the learning of the students and the acquired ability during the course the following tests are planned:

– three intermediate tests (4 hours each)

– in case of failure of the test or upon request of the students a written exam with

three questions: two exercises and a question about theory

– an oral exam with up to three questions

More Information. The students will be welcome to attend 12 (non–mandatory) additional hours of exercises.
1) Differential and difference equation and their properties (hours 4)

Dynamical systems: input, output and state

2) Analysis of linear systems

– Modes (hours 8)

– Stability(hours 4)

– Reachability (hours 8)

– Observability (hours 8)

– Realization (hours 4)

2) Control of linear systems

– Stabilization via state feedback (hours 6)

– Observer design and output stabilization(hours 8)

3) Analysis of nonlinear systems

– generalities (hours 4)

– Equilibrium conditions (hours 2)

– Lyapunov functions and stability analysis (hours 8)

– Linearization (hours 8)

4) Complements

– Optimal control design (hours 4)

– Robustness of dynamical systems (hours 4)

– Model predictive control (hours 2)

– System identification (hours 2)

– Markov chains (hours 4)

– Linear algebra (hours 6)

– Norms, inner product, symmetric matrices (hours 2)

– F. Blanchini, “System and control theory, lecture notes” (English version) (edited by L. Peretti)

– D. Luenberger, “Introduction to Dynamic Systems” (in English)