Stability margins for multilinear interval control systems

A multilinear extension of the result of H. Chapellat and S.P. Bhattacharyya (1989) is given. This result, called the multilinear CB theorem, is useful in determining robust parametric stability and stability margins. The result constitutes a generalization of Kharitonov´s theorem to the case of multilinear interval uncertainty. It provides certain manifolds which capture all the extremal information regarding the uncertainty structure. These extremal manifolds play the same role in analysis and design as the CB segments of S.P. Bhattacharyya (1991) do in the linear case. The usefulness of these CB manifolds is illustrated by an example where it is shown how parametric stability margins can be efficiently calculated