Improving semiquantitative simulation by using Lyapunov analysis

Semiquantitative simulation is a powerful method to analyze uncertain dynamic systems using reasoning techniques. However, simulating systems which exhibit oscillatory behavior, impose big difficulties on the current semiquantitative simulation methods. Reasoning about “energy” can be very helpful for analyzing such systems using semiquantitative simulation. The simulation program QSIM provides such a mechanism, called kinetic-energy filter, which can be used for second order systems of a specific type. This paper proposes a more general approach on the basis of Lyapunov functions. By exploiting the similarities of the descriptions of the system used in semiquantitative simulation and nonlinear control theory it is possible to apply powerful methods for the latter to deduce a Lyapunov function for the system under investigation. Simple yet powerful filtering methods based on Lyapunov functions are presented and demonstrated by example.