TY - GEN A1 - Reis, Timo A1 - Berger, Thomas A1 - Ilchmann, Achim T1 - Normal forms, high gain and funnel control for linear differential-algebraic systems N2 - We consider linear differential-algebraic m-input m-output systems with positive strict relative degree or proper inverse transfer function; in the single-input single-output case these two disjoint classes make the whole of all linear DAEs without feedthrough term. Structural properties - such as normal forms (i.e. the counterpart to the Byrnes-Isidori form for ODE systems), zero dynamics, and high-gain stabilizability - are analyzed for two purposes: first, to gain insight into the system classes and secondly, to solve the output regulation problem by funnel control. The funnel controller achieves tracking of a class of reference signals within a pre-specified funnel; this means in particular, the transient behaviour of the output error can be specified and the funnel controller does neither incorporate any internal model for the reference signals nor any identification mechanism, it is simple in its design. The results are illuminated by position and velocity control of a mechanical system encompassing springs, masses, and dampers. KW - differential-algebraic equations KW - strict relative degree KW - zero dynamics KW - minimum phase KW - stabilization KW - high-gain output feedback KW - funnel control Y1 - 2011 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/871 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-8716 ER -