The final goal of the course is to provide methods to control uncertain linear dynamical systems.

Three main steps are needed to lead the students to such a goal.

First, techniques are provided for the shaping and quantification of the uncertainties, in terms of suitable definition of system norms.

Second, the problem of robust stability at the face of uncertainties are tackled via a Lyapunov function approach.

Finally the problem of feedback control of uncertain systems is deal with through parametrization and model matching synthesis.

Some classical as well as modern techniques will be covered so that the student will acquire the methodological skills to tackle a wide corpus of robust analysis and robust

control problems for uncertain systems.

Lectures and exercise sessions will allow students to:

• Compute the norms of a dynamical system
  
• Check robust stability
• Define a robust control problem in terms of modelization of uncertainties
• Solve a robust control problem via parametrization and model matching
  
• Work out suitable algorithms based on Linear Matrix Inequalities for the points above.

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

Part 1 : Robust performance analysis of uncertain systems 

-  Norm bounded uncertainties and system norms (H2-Hinf)

- Polytopic uncertainties and switching

- Checking robust stability via linear matrix inequalities (LMIs)

- Passivity

- Application examples

Part 2: Robust performance design of uncertain systems

 - Robust H2 control and filtering

 - Robust Hinf control and filtering

 - Switching control (sketch)

-  Robustness in digital implementation (sketch)

- Application examples

Students are required to know the main topics of  system theory and automatic control, included in the course "Advanced and Multivariable Control".

The course comprises lectures and specific sessions with numerical examples.

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

The students should be able to use the learned theoretical and computational tools to solve non trivial analysis and synthesis problems for linear systems affected by both polytopic and norm bounded uncertainties. 

Only for a few chapters

In preparation