Characterizing the solution set of uncertain polynomial systems

Abstract

This paper addresses the estimation of the set of admissible solutions of uncertain polynomial systems with coefficients depending polynomially on an uncertain vector constrained in a polytope. This is a problem relevant to several disciplines, met for instance when investigating the steady states of dynamical systems. It is shown that an outer estimate with fixed shape of this set can be obtained by solving a convex optimization problem with LMI constraints. Then, a necessary and sufficient condition is provided for establishing the tightness of this estimate. Lastly, it is shown how the proposed approach can be extended in order to address the computation of the minimum volume outer estimate in a certain given class. © 2011 Academic Publications, Ltd.