Reliable H_∞ control of uncertain descriptor systems with multiple time delays

The reliable H_∞ controller design problem for uncertain descriptor systems with actuator failures and multiple time delays is investigated. Sufficient conditions to guarantee that the unforced system is regular, impulse-free and exponentially stable are derived. The derived conditions are expressed in terms of a set of linear matrix inequalities, which can be effectively solved by using well known algorithms. Then, based on these results, a reliable H_∞ controller is proposed such that, for all admissible uncertainties and actuator failures occurring among the prescribed subset of faulty actuators, the resulting closed-loop system is regular, impulse-free and exponentially stable with an H_∞ norm bound constraint. The effectiveness of the proposed method is demonstrated by a numerical example.