Robustness analysis: a case study

The stability test of polynomials whose coefficients depend multilinearly on interval parameters is considered. The authors describe and compare four brute-force solution approaches. These are eigenvalue calculation, zero exclusion from a specified value set, algebraic tests of real and complex Hurwitz roots, and the parameter space method. They are applied to a simple example with two parameters and third-order polynomial. An interesting feature of the example is that it can have an isolated unstable point. The example may be useful as a benchmark for future approaches to the multilinear problem. All four methods are shown to be feasible for the simple example, but they require effort.< >