The analysis of piecewise linear dynamical systems

Abstract

The motivation for developing an analysis tool for piecewise linear (PL) systems arose from the desire to model some automotive control systems in a coherent way. These systems appear to have some common properties, in that the system nonlinearities are often represented as piecewise linear functions (e.g. saturation, backlash and relays) and the controllers use logic that can also be treated as piecewise linear functions. This type of system model appears to capture a wide class of complex systems. This observation led to a project at the Control Systems Centre to analyse piecewise linear systems. As a consequence a concept was developed that relies on exploiting the computer as an analysis tool and this idea was tested on the example of a simplified model of an Anti-Lock Braking System (ABS) controlled with a rule-base.

This paper outlines the work done at the Control Systems Centre, UMIST, to develop a basic analysis concept and gives a summary of the efforts to extend the tool to handle as wide a class of systems as possible. The principal conclusions of the ABS example study are also given, as they provide a good insight into the potential of this approach.