An extended-observer approach to robust stabilisation of linear differential-algebraic systems
Thispaperaddressestheproblemofrobustlystabilisingaclassoflineardifferential-algebraic systems char-
acterised by autonomous and asymptotically stable zero dynamics, in spite of parameter uncertainties
ranging over apriori fixed bounded sets. We exploit recent results related to the structural properties and
normal forms of this class of systems and propose a robust control that asymptotically recovers, in practical
terms, the performance of a nominal, though non-implementable, stabilising control. The proposed con-
trol combines a partial output feedback control, aimed at letting the system behave as a regular system,
and a robust control, based on an extended observer, using which the dynamic of the closed loop system
is rendered arbitrarily close to the one of a properly selected stable system. The extended observer, origi-
nally conceived in the context of standard differential systems, is here shown to be the key ingredient for
robustly stabilising the targeted class of differential-algebraic systems.