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.