Exponential stability of solutions to nonlinear time-varying delay systems of neutral type equations with periodic coefficients

Abstract

We consider a class of nonlinear time-varying delay systems of neutral type differential equations with periodic coefficients in the linear terms, d/dt y(t) = A(t)y(t) + B(t)y(t - τ(t)) + C(t) d/dt y(t - τ(t)) + F(t, y(t), y(t - τ(t)), d/dt y(t - τ(t))), where A(t), B(t), C(t) are T-periodic matrices, and ∥F(t, u, v, w)∥ ≤ q1∥u∥ + q2∥v∥ + q3∥w∥, q1, q2, q3 ≥ 0, t > 0. We obtain conditions for the exponential stability of the zero solution and estimates for the exponential decay of the solutions at infinity.