H ∞ dynamical observer-based control for descriptor systems.

This paper addresses the problem of $H_\infty$ observer-based control design for descriptor systems. A new concept of dynamical observer-based control is introduced for linear descriptor systems. The main advantage of this concept is the structure of this dynamical observer, which is more general than those founded in the literature. By using this general structure, particular cases such as the proportional and the proportional-integral observers (PIOs) can be directly deduced. Necessary and sufficient conditions under which the controlled output converges asymptotically to zero are given in a set of linear matrix inequalities formulation. Numerical examples comparing our approach with the proportional and the PIO (deduced from the dynamical observer), and with a functional filter-based controller previously reported in the literature, are respectively presented.