Numerical Methods for Systems and Control : State-Space Techniques and Model Reduction

Friday 6 Mar 2026, 16:30 → Monday 16 Mar 2026, 18:00 Europe/Rome

GSSI

Instructor: Paul Van Dooren (vandooren.p@gmail.com)

Abstract: This short course focuses on numerical linear algebra techniques for basic matrix problems occurring in systems and control. Many of the textbook algorithms in these areas suffer from severe loss of accuracy once implemented numerically. This course describes the most reliable methods and analyzes numerical stability and conditioning of the underlying matrix problems. Applications include identification, analysis, and design problems of systems in state space and polynomial form. Special attention will also be given to the model reduction problem of linear time-invariant systems. The main topics that will be covered:

• Identification of linear time invariant systems
• State-space analysis problems
• State-space design problems
• Polynomial versus state-space models
• Model reduction via projection methods

Schedule:

• Lecture 1 - March 6, 16:30 - 18:00
• Lecture 2 - March 9, 9:00 - 10:30
• Lecture 3 - March 11, 9:00 - 10:30
• Lecture 4 - March 13, 9:00 - 10:30
• Lecture 5 - March 16, 16:30 - 18:00

Prerequisite: A basic course in numerical linear algebra

Textbook: Course notes and a selection of papers.

Useful literature: Thomas Kailath, Linear Systems, Prentice Hall, 1980, Thanos Antoulas, Approximation of large-scale dynamical systems, SIAM, 2005.