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A constructive approach to minimal realization problem of 2D systems

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Abstract

Unlike in the 1D case, it is not always possible to find a minimal state-space realization for a 2D system except for some particular categories. The purpose of this paper is to explore a constructive approach to the minimal Roesser model realization problem for a class of 2D systems which does not belong to the clarified categories. As one of the main results, a constructive realization procedure is first proposed. Based on the proposed procedure, sufficient conditions and explicit construction for minimal realizations of the considered 2D systems are shown. In addition, possible variations and applications of the obtained results are discussed and illustrative examples are presented.

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Authors and Affiliations

  1. The Key Laboratory of Image Processing and Intelligent control, and Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan Hubei, 430074, China

    Huijin Fan

  2. Faculty of Systems Science and Technology, Akita Prefectural University, Akita, 015-0055, Japan

    Hua Cheng & Li Xu

Authors
  1. Huijin Fan
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  2. Hua Cheng
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  3. Li Xu
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Additional information

This work was partly supported by the National Natural Science Foundation of China (No.60604001), and Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (JSPS.KAKENHI 19560448).

Huijin FAN received the B.S. degree in Mathematics from the Central China Normal University, China, in 1995, the M.S degree in Applied Mathematics from the Chinese Academy of Sciences, China, in 1998, and the Ph.D. degree in Electrical Engineering from Nanyang Technological University, Singapore, in 2002.

In 20002, she was a research associate at the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. Then, she joined the National University of Singapore, as a research fellow at the Department of Electrical & Computer Engineering. From April 2004 to July 2005, she was a visiting research fellow at the Department of Electronics and Information Systems, Akita Prefectural University, Akita, Japan. Since August 2005, she has been an associate professor at the Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, China. Her research interests include multidimensional system theory, signal processing and nonlinear stochastic system theory.

Hua CHENG received the B.E. degree from Wuhan University of Science and Technology, Wuhan, China, in 2000, and the M.E. degree from Akita Prefectural University, Akita, Japan, in 2005. She is currently pursing the D.E. degree at Akita Prefectural University. Her research interest is signal processing.

Li XU received the B.E. degree from Huazhong University of Science and Technology, Wuhan, China, in 1982, and the M.E. and D.E. degrees from Toyohashi University of Technology, Toyohashi, Japan, in 1990 and 1993, respectively.

From April 1993 to March 1998, he was an assistant professor at the Department of Knowledge-Based Information Engineering, Toyohashi University of Technology. From April 1998 to March 2000, he was a lecturer at the Department of Information Management, School of Business Administration, Asahi University, Gifu, Japan. Since April 2000, he has been with the Faculty of Systems Science and Technology, Akita Prefectural University, Akita, Japan, where he is currently a professor at the Department of Electronics and Information Systems. His research interests include multidimensional system theory, signal processing and the applications of computer algebra to system theory.

He has been an associate editor for the international journal of Multidimensional Systems and Signal Processing (MSSP) since 2000, and was a guest co-editor for the special issue of “Applications of Gröbner Bases in Multidimensional Systems and Signal Processing” for MSSP published in 2001.

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Fan, H., Cheng, H. & Xu, L. A constructive approach to minimal realization problem of 2D systems. J. Control Theory Appl. 7, 335–343 (2009). https://doi.org/10.1007/s11768-009-7159-6

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  • DOI: https://doi.org/10.1007/s11768-009-7159-6

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