On robust D admissibility for uncertain singular linear systems in generalized linear matrix inequality region

The problem of robust D admissibility in generalized linear matrix inequality regions for uncertain singular linear systems is concerned in this paper. With the introduction of some free matrices, a necessary and sufficient condition for the considered singular linear system to be D admissible is presented in terms of linear matrix inequalities. Based on this, a sufficient condition for the existence of state feedback control law for the resultant closed-loop singular linear systems to be robustly D admissible is proposed and an explicit expression for the desired state feedback control law is also given. The obtained results are expressed in terms of a solution of a set of linear matrix inequalities that can be implemented numerically. Numerical examples illustrate the effectiveness and applicability of our approach.