Structured Stability Margin and the Finite Argument Principle

Abstract

If the structure of the uncertainty in a linear model is known, it is natural to use this information in robustness analysis. In particular, when the model depends on a number of uncertain parameters one sometimes defines a “structured stability margin” measuring the smallest parameter deviation giving instability. There are different definitions of the structured stability Iuargin. They differ in the way the structure of the uncertainty is prescribed. In this article we suggest a new definition that use the probabilistic distribution of the parameters. We will define and calculate a ‘structured stability margin’ which is tailor made to make use of covariance information on parametric uncertainty. Such information is typically obtained from a parametric identification In the calculation of stability margin it is natural to evaluate the characteristic polynomial along the boundary of the stability region. The ‘finite argument principle’ is a tool, which can be used to reduce the number of such evaluations. The frequencies will also automatically concentrate to critical regions. We show explicitly, how the finite argument principle can be used to compute the structured stability margin. An example from robustness analysis of a mechanical system is presented