Dynamic output feedback H ∞ design in finite-frequency domain for constrained linear systems

Abstract

This paper deals with the design problem of H∞ control for linear systems in finite-frequency (FF) domain. Accordingly, the H∞ norm from the exogenous disturbance to the controlled output is reduced in a given frequency range with utilizing the generalized Kalman–Yakubovic–Popov (gKYP) lemma. As some of the states are hard or impossible to measure in many applications, a dynamic output feedback controller is proposed. In order to meet practical requirements that express the limitations of the physical system and the actuator, these time-domain hard constraints are taken into account in the controller design. An algorithm terminating in finitely many steps is given to determine the dynamic output feedback with suboptimal FF H∞ norm bound. The algorithm consists of solving a series of linear matrix inequalities (LMIs). Finally, two case studies are given to demonstrate the effectiveness and advantageous of the proposed method.