H∞ performance analysis and distributed filtering for spatially interconnected systems over specified frequency ranges

ABSTRACTThis paper is concerned with H∞ performance analysis and distributed filtering for spatially interconnected systems (SISs) over specified frequency ranges, including entire frequency (EF) range and finite frequency (FF) range. The main idea is based on a reformed Parseval's theorem for SISs, in which some novel frequency domain spaces and modified Fourier transformations are formulated to explore the various relationships they have with the time domain spaces. After that, an equivalent H∞ frequency domain interpretation for the time domain property of SISs is built, and two numerically verifiable equivalent conditions are formulated to guarantee H∞ performance. Furthermore, we investigate the H∞ performance of SISs over finite frequency range, which is termed as finite frequency (FF) bounded realness for SISs. H∞ Then, the derived results are applied to solve the distributed H∞ filtering problem of SISs, and a practical example is finally given to show the viability of the proposed method.