Estimation of the domain of attraction for polynomial systems via LMIs

Abstract

Investigation of the stability properties of stationary points of nonlinear systems lies at the heart of modern control engineering. In this contribution we show how modern results of real algebraic geometry, a branch of pure mathematics, is used to compute subsets of the region of attraction of asymptotically stable stationary points of polynomial systems. This computation is done in a numerically stable and efficient way by reformulating the problem as a linear matrix inequality (LMI). For this reformulation results from real algebraic geometry are used. The results presented show very clearly that a multidisciplinary approach to nonlinear control systems leads to new insight and new powerful conditions. Some conclusions and an outlook finish the contribution.