Normal forms, high-gain and funnel control for linear differential-algebraic systems
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.