On asymptotic stability of second order differential equations with two commensurate delays (Q6586843)

In this paper, the stability problem for the following second order delay differential equation is considered:\N\[\Ny''(t) = b_0y'(t) + b_1y'(t-\tau) + a_0y(t) + a_1y(t-\tau) + a_2y(t-2\tau),\N\]\Nwhere \(b_0, b_1, a_0, a_1, a_2\) are real constants and \(\tau>0\) is the constant delay. By Pontryagin's theory for quasi-polynomials, the authors find practical necessary conditions for the zero solution to be asymptotically stable. Then sufficient conditions for stability are provided and stability regions for the coefficients are obtained.