Abstract: Stability of time-delay partial differential equations (TDPDE) systems involves 2D quasi-polynomials, while zeros of the characteristic polynomials (2D quasi-polynomials) of TDPDE systems are some continuous and hyper curved surfaces. Zeros are not isolated and separated, leading to difficulty in the stability test of TDPDE systems. To solve the problem, this paper proposes an approach to test asymptotic stability of TDPDE systems by a Hurwitz stability test of 2D characteristic polynomials of the systems. The proposed theorems establish the relationship between the asymptotic stability of TDPDE systems and the Hurwitz stability test of 2D characteristic polynomials, and provide a test approach of the Hurwitz stability test of 2D characteristic polynomials (2D quasi-polynomials). Base on the results, a numerical algorithm with a simpler test procedure for Hurwitz-Schur stability test of 2D quasi-polynomials is developed. An example illustrates the application of the proposed approach.

Key words: time-delay partial differential equation systems, Hurwitz-Schur stability, 2D quasi-polynomials, test algorithm