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IMA Journal of Mathematical Control and Information 1992 9(3):231-244; doi:10.1093/imamci/9.3.231
© 1992 by Institute of Mathematics and its Applications
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On the singular cases of Jury's algorithms for stability testing of linear discrete systems

JASON S. H. TSAI, SHYAN S. CHEN and LEANG S. SHIEH

Control Systems Laboratory, Department of Electrical Engineering, National Cheng-Kung University Tainan 701, Taiwan, Republic of China
Department of Electrical Engineering, University of Houston, Central Campus Houston, Texas 77204-4793, USA

For a stability test of linear discrete systems in a tabular form, two singular cases of Jury's algorithms are considered, in which a row with some (but not all) vanishing leading elements and a row with all zero elements arise respectively. For the singular case of rows with some (but not all) vanishing leading elements, Yeung's method is improved for efficient usages. Based on the newly improved algorithm in treating all-zero rows, the number of roots on the unit circle and their respective orders can be determined. As a result, the situation of conditional stability or instability can be distinguished by the criteria developed in this paper.


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