Kharitonov's theorem and stability test of multidimensional digital filters

Abstract

First, a sufficiency test is developed to test for all the zeros of a polynomial to be within the unit circle when each of its coefficients takes an arbitrary but fixed value within a specified compact interval. This test for robust stability of discrete-time systems is implemented via the use of bilinear transformation and Kharitonov's theorem. Subsequently, this result is used to set up a novel sufficiency test for the stability test of 2-dimensional digital filters. It is shown that the last result can be generalised to stability tests for n-dimensional (n > 2) digital filters. An example is constructed to illustrate the principles of the proposed procedure.