Abstract
This paper is concerned with the H ∞ control problem for singular systems over finite frequency ranges. The disturbance is assumed to be within low-/middle-/high-frequency ranges. Both the state feedback and static output feedback controllers are designed. First, by combining the Lyapunov function method and the generalized Kalman–Yakubovich–Popov lemma, a new finite frequency bounded real lemma (BRL) is proposed, which ensures the resulting closed-loop system to be regular, impulse free and stable with given finite frequency H ∞ performance bound. It is shown by theoretical analysis and numerical simulation that the proposed BRL has less conservatism than the existing ones in the literature. With the aid of the Finsler's Lemma, two improved finite frequency BRLs are further presented for the design of controllers. Then, by utilizing convexification techniques, sufficient conditions for solving the desired state feedback and static output feedback gains are presented in terms of linear matrix inequalities, respectively. Finally, the applicability and effectiveness of the proposed control methods are verified by a 6-bus power network system.
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