Finite frequency memory output feedback controller design for discrete-time systems with state multiplicative noises

This article studies the problem of output feedback control for discrete-time systems with state multiplicative noises. Aiming at reducing the controller design conservatism, a novel finite frequency memory control approach is developed, which makes full use of both current and past output measurements together with the frequency spectrum information of disturbances. By augmenting the control input into the closed-loop system state, a descriptor system approach is proposed to facilitate the controller synthesis. Then, based on the Fourier transform, Parseval's relation, and Projection lemma, the linear matrix inequalities (LMIs)-based controller design results are obtained to guarantee the mean-square asymptotic stability with finite frequency H-infinity performance for the resulting closed-loop system. The effectiveness of the developed approach is validated by an antenna motion control system.