New sufficient conditions are derived for stability robustness of linear time-invariant state-space systems with constant real parameter uncertainty. These bounds are obtained by applying a guardian map to the uncertain system matrices. Since this approach is only valid for constant real parameter uncertainty, these bounds do not imply quadratic stability, which guarantees robust stability with respect to time-varying uncertainty but is often conservative with respect to constant real parameter uncertainty. Numerical results are given to compare the new bounds with bounds obtained previously by means of Lyapunov methods.