Extended H2 output feedback control for continuous descriptor systems

This paper investigates the design of an “extended” H₂ output feedback controller for continuous descriptor systems. In such problem, the controller, which is described within descriptor framework, has to satisfy simultaneously two conditions: 1-The closed-loop is admissible and has minimum H₂ norm. 2-Only the internal stability of a part of the closed-loop is sought. In such case, the standard H₂ output feedback control problem for descriptor systems cannot be solved. An explicit characterization of the optimal solution, based on two generalized algebraic Riccati equations (GAREs) and two structured generalized Sylvester-type equations, is given. A numerical example is included to illustrate the applicability of the proposed results.