In this paper, a new result on the robust stability region construction in the parameter space of linear uncertain systems is presented. Based on the concept of coordinate transformations in the parameter space and a simple optimization technique, the new stability analysis result is then extended for constructing a union of hyperellipsoids with larger and larger volumes to approximate the whole robust stability region in the parameter space. The computational process involves only simple algebraic operations of matrices, singular value decompositions, and solutions of Lyapunov equation. Thus, the method can be easily programmed using existing software packages. This approach is applicable to linear systems described by state‐space models and high‐order differential equations. Some numerical examples are included to illustrate the method.