A finite test algorithm for 2D Schur polynomials based on complex Lyapunov equation

Using finite length of DFT, classical frequency tests only obtain an approximate conclusion for the Schur stability of given 2D polynomials, and generally, their finite algorithm implementations are necessary conditions only due to the finite length of DFT. Though algebraic tests have no such problem, they can not process high order 2D polynomials. Based on the complex Lyapunov equation and ∞-norm of matrices, we establish a new sufficient condition for 2D Schur polynomials. Based on the condition, we develop a finite frequency test algorithm for Schur stability of 2-D polynomials, which can avoid the above problems existing in present frequency and algebraic tests. Examples are given to illustrate its application