Zero dynamics and funnel control of general linear differential-algebraic systems

Abstract

We study linear differential-algebraic multi-input multi-output systems which are not necessarily regular and investigate the zero dynamics and tracking control. We introduce and characterize the concept of autonomous zero dynamics as an important system theoretic tool for the analysis of differential-algebraic systems. We use the autonomous zero dynamics and ( E, A, B )-invariant subspaces to derive the so called zero dynamics form – which decouples the zero dynamics of the system – and exploit it for the characterization of system invertibility and asymptotic stability of the zero dynamics. A refinement of the zero dynamics form is then used to show that the funnel controller (that is a static nonlinear output error feedback) achieves – for a special class of right-invertible systems with asymptotically stable zero dynamics – tracking of a reference signal by the output signal within a pre-specified performance funnel. It is shown that the results can be applied to a class of passive electrical networks.