International School 2008 in Monopoli

Linear System Theory is basic in the study of dynamics, control, and signal processing. The aim of this summer school is to provide a coherent set of lectures that explain aspects of this theory, with special emphasis on recent developments and computational methods. However, in order to make the course reasonably self-contained, several general background lectures are also included.

Mathematical models in general, and linear dynamical systems in particular, allow a multitude of representations. The behavioral approach offers a framework that unifies these representations. The behavior declares which phenomena are, according to the model, possible.  In the context of dynamical systems, the behavioral equations are often differential equations. In the linear time-invariant case, many different representations have emerged, among them kernel representations, image representations, transfer functions, input/state/output representations, and equations with rational symbols. Special representations allow to characterize system properties. For example, a linear time-invariant system is controllable if and only if it allows an image representation, and stabilizable if and only if it allows a representation with a rational symbol that is left prime.  The behavioral approach to dynamical systems is one of the main themes of the course.

This diversity of representations leads to an interplay between various model classes, especially between state models that code the internal dynamics, and convolutions or differential equations that code the external dynamics. State construction is one of the main topics of the course, leading to algorithms based on the Hankel matrix and several model reduction methods that allow to simplify the complexity of a model. System identification refers to the problem of finding a dynamical model directly on the basis of measured data.  Various system identification algorithms are presented. The course also deals with control problems, especially with robust control and  associated convex optimization  methods.

There will be computers and Matlab available for the students at the exercise sessions.

The school is addressed to graduate students, PhD students, young researchers in scientific disciplines (Mathematics, Statistics, Physics, Engineering, Computer Science, ...).

Lecturers