Controlled invariance for DAEs

Abstract

We study the concept of locally controlled invariant submanifolds for nonlinear descriptor systems. In contrast to classical approaches, we define controlled invariance as the property of solution trajectories to evolve in a given submanifold whenever they start in it. It is then shown that this concept is equivalent to the existence of a feedback which renders the closed‐loop vector field invariant in the descriptor sense. This result is motivated by a preliminary consideration of the linear case. Local controlled invariance leads to the concept of output zeroing submanifolds. We show that the outcome of the differential‐algebraic version of the zero dynamics algorithm yields a locally maximal output zeroing submanifold. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)