Two equivalent sets: Application to singular systems

In this paper, we consider the problem of state feedback control design for continuous singular systems by applying equivalent sets technique. A new formulation of dissipativity condition is proposed. Based on this condition, the desired state feedback controller is designed such that the closed-loop system is admissible and dissipative. For singular Markovian systems, necessary and sufficient conditions are proposed for the system to be admissible and for the state feedback control design. For time-delay singular Markovian systems, a new bounded real lemma is proposed and the corresponding H∞ control problem is studied. Numerical examples are given to illustrate the effectiveness of the theoretic results developed.