Design of positive real controller for continuous-time descriptor systems with impulse

For the continuous-time descriptor system, an extension of the positive real lemma is derived by constructed method. Using algebraic transformations into the second restricted equivalent description system, the state feedback controller is designed via the solvability of linear matrix inequality (LMI). Furthermore, in the conditions of controllability and observability, the positive realness of the closed loop system can be guaranteed and the impulse can be eliminated by adding control variables. Numerical simulation is carried out to show the efficiency.