Zero dynamics and funnel control of general linear differential-algebraic systems
We study linear differential-algebraic multi-input multi-output systems which are not necessarily regular and investigate the zero dynamics and tracking control. We use the concepts of 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. Asymptotic stability of the zero dynamics is characterized and some implications for stabilizability in the behavioral sense are shown. A refinement of the zero dynamics form is then exploited 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.
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