9 credits ECTS


Mathematical Models. State space representations. Linear models. Nonlinear models and its linearization around equilibrium points and solutions.

TIme domain analysis. Output and state free response. Natural modes and modal decomposition. State and output forced response. Impulsive and step response. Rise time, settling time and maximal overshooting and undershooting.

Frequancy domain analysis. Fundamental properties of Laplace transform and most used transforms. Transfer functions. Input-output models.

Stability of linear systems: main notions and criteria. Routh criterion.

Bode plots. Armonic response. Steady state and transient response with sinusoidal and polynomial inputs.

Controllability and observability. Controllability and observability Grammian. State-to-state controllability and state reconstruction. Hautus tests for controllability and observability.

Time domain design. Eigenvalue assignment and state estimation and reconstruction. Steady state performances: output regulation and regulator equations.

Interconnected systems: series, parallel and feedback interconnections. General properties of feedback interconnections. Zero-pole cancellations.

Stability of linear feedback systems. Polar plots and Nyquist criterion.

Frequency domain design. Proportional, derivative and integral control actions. Steady state performance: tracking and disturbance compensation. Transient performances: phase margin and cross-over frequency versus cut-off frequency and resonce peak. Zero-pole control actions for phase margin and cross-over frequency modification.

Root-locus. Stabilization and pole assignment with root-locus methods.


Pages and proofs to be omitted in the text:

- proof propositions 6.2.3, 6.2.4, 6.2.5

- proof theorems 6.2.1, 7.0.1

- paragraph 7.3

- chapter 9 except definitions of controllability matrix,

observability matrix, controllable and observable systems.

- proof lemma 10.1.1 and 10.1.2, proposition 10.2.1

- proof propositions 10.4.1

-proof proposition 14.2.2

- proof rules (V) and (VI) paragraph 16.1

- paragraph 16.3.5

- all proofs of the appendices A,B,C,D.

Supplementary exercise texts (optional)

Supplementary theoretical texts (optional)


Support and auxiliary material

Supplementary material to the text (.pdf files)

Simple MATLAB programs (.m files)

Supplementary material to control design (.pdf files)

Written exams (.pdf files in italian)

Written exams (.pdf files in english)

Student hours: each Friday from 3 p.m. to 6 p.m. (Via Ariosto 25 - Room A207)

Attendance certificates (for work)

Forms must be downloaded, filled up and delivered to the teacher for sign.

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