On the double bilinear transformation and nonessential singularities of the second kind at infinity

This paper addresses the BIBO (bounded-input bounded-output) stability of a class of discrete 2-D transfer functions in the presence of nonessential singularities of the second kind (NSSK´s) on the unit bidisk. Conditions under which the double bilinear transformation (DBT) preserves stability are derived. The results presented here also extend the class of systems whose stability can be predicted. Use of the inverse DBT to produce a continuous equivalent of the discrete 2-D transfer function allows easy application of a continuous-domain equivalent of a criterion developed by Dautov. The necessary and sufficient condition for stability derived in this work provides a simple check for the class of systems under consideration