Kybernetika 38 no. 5, 643-656, 2002

Rank-one LMI approach to robust stability of polynomial matrices

Didier Henrion, Kenji Sugimoto and Michael Šebek


Necessary and sufficient conditions are formulated for checking robust stability of an uncertain polynomial matrix. Various stability regions and uncertainty models are handled in a unified way. The conditions, stemming from a general optimization methodology similar to the one used in $\mu$-analysis, are expressed as a rank-one LMI, a non-convex problem frequently arising in robust control. Convex relaxations of the problem yield tractable sufficient LMI conditions for robust stability of uncertain polynomial matrices.