On an Inviable Approach for Derivation of 2-D Stability Tests

A tabular stability test for two-dimensional (2-D) discrete systems that was published in these Transaction is shown to be not correct. It is also shown that the claimed new method that it introduced to extend stability conditions from one-dimensional (1-D) to 2-D systems relies on a mathematically inviable argument. The paper tries to find a similar but correct algorithm and stability conditions. The outcome of the search after a stability test with similar algorithm is a variant of the MariaFahmy 2-D stability test for which a more concise set of necessary and sufficient conditions for stability are obtained. The search after stability conditions of similar appearance that can be posed on the correct algorithm, yields new necessary conditions for 2-D stability that resemble stability conditions associated with the “reflection coefficient” parameters in the 1-D Schur test.