Passivity and Finite-Gain Performance for Two-Dimensional Digital Filters: The FM LSS Model Case

Abstract

This brief considers the two-dimensional (2-D) passivity performance analysis problem of 2-D digital filters in the Fornasini–Marchesini local state–space (FM LSS) form. The purpose is to establish a new criterion in terms of linear matrix inequality such that the 2-D digital filters in the FM LSS form ensure 2-D passivity performance with a storage function. Moreover, this brief reveals that the 2-D digital filters exhibit the 2-D finite-gain performance under the proposed criterion. Without interference, the criterion guarantees the asymptotic stability of 2-D digital filters. An application example to a 2-D low-pass filter is given to demonstrate the usefulness of the presented passivity criterion. The criteria in this brief and in a previous work of one of the authors, as a whole, give methodical results for the 2-D passive removal of the overflow oscillation of 2-D digital filters with external inferences.