Detectability and observer design for linear descriptor systems

In this paper, a method is proposed to design Luenberger type observer for a class of linear descriptor systems satisfying complete detectability condition. The method is based on the properties of restricted system equivalent, derived here from a given descriptor system by means of simple matrix theory. Using restricted system equivalent form, equivalence between the detectability of a given descriptor system and that of a normal system has been established. Coefficient matrices of the proposed observer have been synthesized using pole placement technique of normal system theory and LMI approach based on the Lyapunov stability theory.