In various modern linear control systems, a common practice is to make use of control in the feedback loops which act as an important tool for linear feedback systems. Stability and instability analysis of a linear feedback system give the measure of perturbed system to be singular and non-singular. The main objective of this article is to discuss numerical computation of the $\mu$ -values bounds by using low ranked ordinary differential equations based technique. Numerical computations illustrate the behavior of the method and the spectrum of operators are then numerically analyzed.