On the Computation of Value Sets for Robust Stability Analysis

Abstract

Robust stability problems arise, if a system dependds on uncertain parameters. For a large number l of parameters conventional methods break down. However, if the system allows a "tree-structured decomposition" of its characteristic polynomial P(s,q) or an equivalent rational chracteristic equation R(s,q) then the complex value sets respectively can be computed and displayed very fast and robust stability test by zero exclusion of the value set can be performed by inspection. We show how to execute computer aided value set operations and demonstrate for exmples of mass-spring damper systems how to preserve tree structures in technical systems. For an example with 51 parameters the computation of the value set at on frequency takes 17 seconds.