2-D representation and generalized Kalman-Yakubivich-Popov lemma of one dimensional spatially interconnected systems

This paper presents a 2-D hybrid Roesser model for a class of spatially interconnected systems (SISs) in one spatial dimension. The generalized Kalman-Yakubivich-Popov (KYP) lemma for 2-D hybrid Roesser model is developed, which plays a significant role in the system control and synthesis. As two important applications of the new KYP lemma, the finite frequency bounded realness and positive realness are considered. The results of this paper can be generalized to the class of SISs whose model is in higher spatial dimension.