Finite frequency test for Hurwitz 2-D polynomials

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