A LOW RANK ODE BASED TECHNIQUE FOR NUMERICAL APPROXIMATION OF LOWER BOUNDS OF STRUCTURED SINGULAR VALUE

Abstract

The structured singular value is a well-known mathematical quantity which plays a vital role in the investigation of the stability, instability, robustness and performance of linear input and output systems in control. We present an iterative method for the approximation of the lower bounds of structured singular values. The iterative method is based on low rank ordinary differential equations and is restricted to performing when pure complex full block uncertainties are under consideration. Numerical experimentation shows the behavior of lower and upper bounds of structured singular values. Furthermore, we investigate and analyze graphically the behavior of eigenvalues and singular values. The pseudospectrum of three-dimensional real valued matrices is inspected with the help of EigTool.