A Mathematical Tool to Investigate the Stability Analysis of Structured Uncertain Dynamical Systems with M-Matrices

The μ-value or structured singular value is a prominent mathematical tool to analyze and synthesize both the robustness and performance of time-invariant systems. We establish and analyze new results concerning structured singular values for the Hadamard product of real square M-matrices. The new results are obtained for structured singular values while considering a set of block diagonal uncertainties. The targeted uncertainties are of two types, that is, pure real scalar block uncertainties and real full-block uncertainties. The eigenvalue perturbation result is utilized in order to determine the behavior of the spectrum of perturbed matrices (A∘B)Δ(t) and ((A∘B)TΔ(t)+Δ(t)(A∘B)).