IJPAM: Volume 70, No. 4 (2011)

CHARACTERIZING THE SOLUTION SET OF
UNCERTAIN POLYNOMIAL SYSTEMS

Graziano Chesi
Department of Electrical and Electronic Engineering
University of Hong Kong
HONG KONG


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.

Received: November 7, 2010

AMS Subject Classification: 12D10, 93C10, 15A39

Key Words and Phrases: uncertain polynomial systems, linear matrix inequality (LMI)

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 70
Issue: 4