摘要
This paper first gives necessary and sufficient conditions of asymptotic stability independent of delay (ASi. o. d. ) of a certain class of symmetric differential systems with commensurate or non -commensurate delays. These conditions give equivalent relationship between the Asi. o. d. of delay systems and the asymptotic stability of ordinary differential systems with special complex coefficients. Then a sufficient condition for the Asi. o.d. of symmetric retarded system is obtained in terms of negative definiteness of a real symmetric matrix. Finally, examples are shown to demonstrate the effectiveness of the proposed method.
This paper first gives necessary and sufficient conditions of asymptotic stability independent of delay (ASi. o. d. ) of a certain class of symmetric differential systems with commensurate or non -commensurate delays. These conditions give equivalent relationship between the Asi. o. d. of delay systems and the asymptotic stability of ordinary differential systems with special complex coefficients. Then a sufficient condition for the Asi. o.d. of symmetric retarded system is obtained in terms of negative definiteness of a real symmetric matrix. Finally, examples are shown to demonstrate the effectiveness of the proposed method.
