H∞ Control Designs for Continuous-Time Singular Systems

This paper investigates some H∞ control problems for linear continuous-time singular systems. The objective is to design controllers that guarantee the admissibility of the closed-loop system and simultaneously achieve a prescribed H∞ disturbance attenuation level. To this end, a framework based on novel strict LMIs (Linear Matrix Inequalities) is developed using a Lyapunov function approach for the analysis of admissibility and H∞ performance. In particular, an additional scalar parameter α is introduced to generalize the condition reported in previous results in the literature, providing greater flexibility. Then, sufficient LMI conditions are derived for the synthesis of both state-feedback and static output-feedback controllers. Finally, some numerical examples demonstrate the effectiveness of the proposed method.