Computer algebra methods for testing the structural stability of multidimensional systems

Abstract

In this paper, we present new computer algebra based methods for testing the structural stability of n-D discrete linear systems (with n ≥ 2). More precisely, starting from the usual stability conditions which resumes to deciding if an hypersurface has points in the unit polydisk, we show that the problem is equivalent to deciding if an algebraic set has real points and use state-of-the-art algorithms for this purpose. Our strategy has been implemented in Maple and its relevance demonstrated through numerous experimentations.