Robustness analysis: a case study

Abstract

Linear systems with uncertain parameters q are analyzed for stability for all q in a box Q. An example with multilinear dependency of the characteristic polynomial P(s, q) on the parameters is used as a test case for the composition of four methods: (1) eigenvalues (s-plane), (2) zero exclusion from the complex value set (P-plane), (3) algebraic test of Hurwitz conditions, and (4) parameter space (stability boundary exclusion from Q in projected q-space). The methods are also discussed with respect to gridding, graphical warning for singular cases, extension to many parameters, extension to polynomic coefficient functions, extension to Gamma -stability, and insight beyond a yes-no answer to the analysis problem.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>