Reduced-order H∞ controller design for descriptor systems

State-space formulas for the reduced-order H_∞ controllers for descriptor systems are given. The approach taken is mainly based on the solutions of two generalized algebraic Riccati equations (GARE), while exploiting the structure of the deflating subspace of the pencil {E, W_∞}, where W_∞ is an admissible solution to a GARE that is the descriptor systems counterpart of a certain ARE (algebraic Riccati equation) first developed by Petersen et al. (1991). This approach has the advantage that, by proper selection of the bases of the deflating space and suitable assumptions, the reduced-order controller may be in a normal form, namely the E-matrix of the controller is nonsingular