93D21 Adaptive or robust stabilization
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- 2011 (1)
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- differential-algebraic equations (1)
- funnel control (1)
- high-gain output feedback (1)
- minimum phase (1)
- stabilization (1)
- strict relative degree (1)
- zero dynamics (1)
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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.