Robust Observer-Based Controller Design for Uncertain Discrete-time Systems in Finite Frequency Domain

In this paper, the problem of finite frequency observer-based controller design for uncertain linear discrete-time systems is investigated with the use of the Generalized Kalman Yakobovich Popov (GKYP) lemma. A new condition guaranteeing the finite frequency controller design for discrete-time systems is derived, in terms of Linear Matrix Inequalities (LMIs). This study reduces the conservatism of the existing full-frequency design and includes it as a special case. In the end, an example is provided, to show the effectiveness of the derived results.