Abstract: For a linear or nonlinear system affected by real parametric uncertainty, this paper focuses on robust stability analysis via the Lyapunov stability theory. In this paper, the robust stability theorems presented ensure sufficient conditions for the robust stability of the system with real parametric uncertainty. With the help of Maple and Gloptipoly, two new stability algorithms based on the theorems give the range of the values of uncertain real parameters for linear systems and nonlinear systems respectively. In addition, the paper includes three examples that describe the application of the stability theorems.