Kalman-Yakubovich-Popov Lemma for Two-Dimensional Systems
| Authors: | Yang Ran, The University of Melbourne, Australia
Xie Lihua, Nanyang Technological University, Singapore
Zhang Cishen, Nanyang Technological University, Singapore |
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| Topic: | 1.1 Modelling, Identification & Signal Processing |
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| Session: | Advances in Systems Theory and Nonlinear Filtering |
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| Keywords: | Two-dimensional systems, Kalman-Yakubovich-Popov Lemma, digital filters, Bounded and positive realness |
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Abstract
This paper is concerned with the development of a version of Kalman-Yakubovich-Popov (KYP) lemma for two-dimensional (2-D) systems characterized by the Roesser model. We shall establish the 2-D KYP lemma over any given finite frequency range which contains the KYP lemma over the infinite frequency range as a special case. Note that the latter has not been known for 2-D systems even though its one-dimensional (1-D) counterpart has been available for a long time. Our result is given in terms of a linear matrix inequality (LMI) which enables efficient computations for both analysis and design. As important applications of the lemma, 2-D bounded realness and positive realness will be investigated. A numerical example on the design of 2-D digital filter will be demonstrated.
