$H_{\infty}$ Filter Based Functional Observers for Descriptor Systems

This paper considers the
$H_{\infty}$
observers design problem for linear time-invariant descriptor systems. A sufficient condition is established for functional observers of order equal to the dimension of the vector to be estimated. This sufficient condition is milder than the other existing conditions in the literature. Furthermore, the observers are of the state space form, and the parameter matrices' existence is proved via elementary matrix theory. It is shown that the observer parameter matrices exist if a matrix equation is solvable. The solution of this matrix equation is not unique, and this non-uniqueness is utilized to meet other specifications of the observer via the solution theory of linear matrix inequalities (LMIs). The theoretical findings are illustrated by designing a functional observer for an electric circuit.