H∞ dynamical observers design for linear descriptor systems. Application to state and unknown input estimation

The present paper considers the H∞H∞ observers design problem for descriptor systems. The goal is to design a dynamical observer such that the resulting dynamic estimation error is stable while the transfer function from the disturbance input to this error satisfies a prescribed H∞H∞ norm level. Conditions for the solvability of this problem are obtained in terms of a set of linear matrix inequalities (LMIs). An extension to a simultaneous estimation of state and unknown input for descriptor systems is presented. A numerical example is provided to illustrate our approach.