The linear continuous-time systems to be discussed are described by state space models with structured time-varying uncertainties. First, the explicit maximal perturbation bound for maintaining quadratic Lyapunov stability of the closed-loop systems is presented. Then, a robust design method is proposed. Given an open-loop, nominal system with information of the uncertainty structure, the proposed robust design method produces a linear constant output feedback control law which maximizes the perturbation bound for maintaining quadratic Lyapunov stability. Both the optimal results for robust analysis and robustness design can be obtained by using an efficient numerical algorithm (e.g. minimax of MATLAB) with analytic gradients given in this paper. Examples are investigated in some detail to show the improvements and advantages of the proposed methods over previous ones.