The paper introduces a general approach for analyzing linear systems with structured uncertainties using a new generalized spectral theory for matrices. This approach extends techniques based on singular values and addresses the limitations of these methods, particularly in handling large perturbations and simultaneous input/output uncertainties. The main theoretical results are presented in Sections 3-5, including the formulation of the block-diagonal perturbation problem, the definition and properties of the function \(\mu\), and the computation of gradients for singular values. The paper also discusses the importance of structured uncertainties in multivariable feedback systems and provides examples to illustrate the application of the proposed methods. The results are intended to contribute to better techniques for handling structured uncertainty in feedback systems and to advance the understanding of multiloop feedback systems.The paper introduces a general approach for analyzing linear systems with structured uncertainties using a new generalized spectral theory for matrices. This approach extends techniques based on singular values and addresses the limitations of these methods, particularly in handling large perturbations and simultaneous input/output uncertainties. The main theoretical results are presented in Sections 3-5, including the formulation of the block-diagonal perturbation problem, the definition and properties of the function \(\mu\), and the computation of gradients for singular values. The paper also discusses the importance of structured uncertainties in multivariable feedback systems and provides examples to illustrate the application of the proposed methods. The results are intended to contribute to better techniques for handling structured uncertainty in feedback systems and to advance the understanding of multiloop feedback systems.