On the singular cases of Jury's algorithms for stability testing of linear discrete systems

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.