N-D representation and generalised Kalman–Yakubivich–Popov lemma of spatially interconnected systems with interconnected chains

This paper presents a multidimensional (N-D) hybrid Roesser model for a class of spatially interconnected systems (SISs) with interconnected chains. A generalised Kalman–Yakubivich–Popov (KYP) lemma for N-D hybrid Roesser model is developed, which plays a significant role in the system control and synthesis. As the application of the developed generalised KYP lemma, robust finite-frequency H∞ filter problem for SISs with interconnected chains is studied. Moreover, it is shown that the developed finite-frequency filter design methods are generally less conservative than the entire frequency ones. Finally, a practical example is provided to validate the effectiveness of the proposed method.