Approximating structured singular values for Chebyshev spectral differentiation matrices

Abstract

In this article, we present the numerical computation of lower bounds of structured singular value known as the µ-value for a family of Chebyshev spectral differentiation matrices. The µ-value is a versatile tool used in control in order to analyze the robustness, performance, stability, and instability of feedback systems in system theory. The purposed methodology is based upon low-rank ordinary differential equations based technique and provides tight lower bounds of µ-value once compared with the well-known MATLAB routine mussv available in the MATLAB control toolbox.