On the Computation of Value Sets for Robust Stability Analysis

Abstract

Robust stability problems arise, if a system depends on uncertain parameters. For a large number of parameters conventional methods break down. However, if the system allows a "tree-structured decomposition" of its characteristic polynomial or an equivalent rational characteristic equation, then the complex value sets respectively can be computed and displayed very fast and a robust stability test by zero exclusion from the value set can be performed by inspection. In this paper we show how to execute computer aided value set operations and demonstrate by way of mass-spring-damper systems how to preserve tree structures in technical systems