# ECS Intranet:

Algebraic and Behavioural Systems Theory

Control systems are described by equations (eg differential
equations), but their properties of interest are most naturally
expressed in terms of the system trajectories (the set of all
solutions to the equations). This is formalized by the relatively
new notion of the system **behaviour**, due to Willems. The
manipulation of system equations on the other hand can be formalized
using algebra, more precisely module theory for linear systems. The
relationship between modules and behaviours is very rich and leads
to deep results on system structure.

The aim of this project is to investigate this module-behaviour correspondence and apply it to deepen our understanding of control systems theory and address outstanding problems. We are particularly interested in the application area of multidimensional systems, i.e. systems described by partial differential equations or the discrete equivalent. In this area, we have to date had much success using these tools, eg in the characterization of controllability, the definition, characterization and decomposition of system poles, and the investigation of the relationship between feedback and trajectory control. Current areas of work include the extension to systems with variable coefficients, and the development of a general theory of model reduction and system identification for such systems.

**Homepage**: http://www.isis.ecs.soton.ac.uk/control/projects/abst/abst.htm**Type**: Normal Research Project**Research Group**: Information: Signals, Images, Systems Research Group**Theme**: Control Systems**Dates**: 1st October 1995 to ?

### Funding

- Royal Society
- EPSRC

### Principal Investigators

You can edit the record for this project by visiting http://secure.ecs.soton.ac.uk/db/projects/editproj.php?project=87