Generalized Two-Dimensional Kalman–Yakubovich–Popov Lemma for Discrete Roesser Model

Kalman-Yakubovich-Popov (KYP) lemma has played a significant role in one-dimensional systems theory. However, there has been no two-dimensional (2-D) KYP lemma in the literature, even for the infinite frequency domain. This paper develops a generalized KYP lemma for 2-D systems described by discrete Roesser model. The generalized KYP lemma relates frequency-domain properties of the 2-D system, such as positive realness and bounded realness over any given rectangular frequency domain, to a linear matrix inequality, enabling efficient computation for both the analysis and the design. As special cases of the lemma, 2-D bounded realness and positive realness are investigated. Numerical examples on the design of 2-D digital filters are given to demonstrate the relevance of the lemma.