Generalised Kalman–Yakubovich–Popov lemma with its application in finite frequency positive realness control for two‐dimensional continuous‐discrete systems in the Roesser model form

Abstract

This study is concerned with the problem of generalised Kalman–Yakubovich–Popov (GKYP) lemma and its application to two-dimensional (2D) continuous-discrete systems described by Roesser model. On the basis of the feature of states in the system, a rectangular finite frequency range is characterised by a linear matrix inequality and then combined with 𝒮-procedure, the GKYP lemma is developed for 2D continuous-discrete systems in Roesser model. As special cases of this lemma, 2D continuous-discrete case finite frequency bounded realness and positive realness are investigated as well. Furthermore, the finite frequency 2D positive realness control problem via state-feedback controllers are considered based on the developed lemma. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.