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

Abstract

This article considers the finite-frequency (FF) H2-H∞ composite control problem for continuous singularly perturbed systems. To address the performance requirements in the low-and high-frequency ranges, the FF H2 and H∞ norms are used to impose on the performance of the slow and fast subsystems, respectively. The FF H2 control of the slow subsystem is analyzed using the FF Gramian matrix method. While the FF H∞ control of the fast subsystem is studied by using the Generalized Kalman-Yakubovic̆-Popov Lemma. Subsequently, an H2-H∞ 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.