A Simple Method to Determine the Stability and Margin of Stability of 2-D Recursive Filters

In this paper we propose some simple numerical algorithms for stability testing of 2-D recursive digital filters and estimation of their margin of stability. The basic idea is to take one variable as a parameter and to make the system a continuous function of this parameter. We then find the critical values of the parameter under which the system becomes unstable. The critical values can be computed via checking singularity of the Sylvester resultant matrix or Kronecker sum in some specific domains. This is equivalent to solving a generalized eigenvalue problem. If a filter is stable, the estimation of the margin of stability can be obtained simply by scaling these two variables. If a filter is unstable this algorithm will show all the poles in the unit bidisk and will give the maximal analytic bidisk as well. Three examples are given to show the effectiveness of the algorithm.