Using Global Properties for Qualitative Reasoning: A Qualitative System Theory

1 Abstract All the qualitative simulation algorithms so far proposed depend upon local propagation paradigm, and hence produce spurious states. Recent approaches use topological constraints in phase space diagrams for filtering the spurious states. We propose an alternative method of recognizing global properties in the graphically expressed qualitative model. Qualitative versions of such system-theoretic concepts as stability and observability are used to analyze the global properties of the system. We first present structural conditions for recognizing qualitative stability or instability in the qualitative model. We introduce the new concept of invariant sign pattern which is a qualitative version of fixed point. Once the qualitative model becomes the invariant sign pattern , it remains in that state. The conditions for the qualitative model to have an invariant sign pattern are also characterized. Although our method is restricted to a linear system, the method does not suffer from such restrictions coming from two dimensional phase space diagrams , such as the target system must be a second order system. We also discuss how to extend the method to non-linear systems.