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

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.