H₂-H∞ Composite Control for Singularly Perturbed Systems With Finite-Frequency Performances

This article considers the finite-frequency (FF) $H_{2}$ - $H_{\infty }$ composite control problem for continuous singularly perturbed systems. To address the performance requirements in the low- and high-frequency ranges, the FF $H_{2}$ and $H_{\infty }$ norms are used to impose on the performance of the slow and fast subsystems, respectively. The FF $H_{2}$ control of the slow subsystem is analyzed using the FF Gramian matrix method. While the FF $H_{\infty }$ control of the fast subsystem is studied by using the Generalized Kalman-Yakubovič-Popov Lemma. Subsequently, an $H_{2}$ - $H_{\infty }$ composite controller for the singularly perturbed system is developed. Finally, two simulation examples involving an armature control direct-current motor system are demonstrated to verify the effectiveness and superiority of the proposed control scheme.