Estimates for the Norm of Green's Matrix Based on the Integral Performance Criterion for Dichotomy and Hausdorff Set Bounds

For a system of ordinary differential equations of the form $du/dt=Au+f(t)$, $-\infty <t<\infty$, we obtain new upper bounds for the second norm of Green's matrix using the integral performance criterion for dichotomy and bounds of the Hausdorff set of the matrix A. These estimates are considerably better for many applications than some well-known ones.