This paper introduces a general approach for analyzing linear systems with structured uncertainties based on a new generalized spectral theory for matrices. The results extend singular value methods, eliminating their most serious limitations. The paper focuses on multivariable feedback systems, where traditional single-loop analysis is insufficient. It addresses the challenge of evaluating sensitivity and robustness in the presence of structured uncertainties, particularly in multiloop systems where signals and responses vary with both frequency and direction. Singular-value methods, while useful, are limited to a specific class of uncertainties and cannot account for the directionality of perturbations in multiloop systems. The paper proposes a function μ that provides necessary and sufficient conditions for structured matrix perturbation problems. This function is defined in terms of the matrix determinant and is used to analyze the robustness of systems with arbitrary constraints on their structure. The paper also develops tools for computing gradients of singular values, which are used to compute μ in special cases. The results are applied to analyze systems with simultaneous input and output perturbations, and the paper provides examples and computational experience to illustrate the effectiveness of the proposed methods. The key findings include the development of a function μ that can be used to analyze systems with structured uncertainties, and the demonstration that the function μ is related to the spectral radius and maximum singular value. The paper concludes that the proposed methods provide a more accurate and reliable analysis of multivariable feedback systems with structured uncertainties.This paper introduces a general approach for analyzing linear systems with structured uncertainties based on a new generalized spectral theory for matrices. The results extend singular value methods, eliminating their most serious limitations. The paper focuses on multivariable feedback systems, where traditional single-loop analysis is insufficient. It addresses the challenge of evaluating sensitivity and robustness in the presence of structured uncertainties, particularly in multiloop systems where signals and responses vary with both frequency and direction. Singular-value methods, while useful, are limited to a specific class of uncertainties and cannot account for the directionality of perturbations in multiloop systems. The paper proposes a function μ that provides necessary and sufficient conditions for structured matrix perturbation problems. This function is defined in terms of the matrix determinant and is used to analyze the robustness of systems with arbitrary constraints on their structure. The paper also develops tools for computing gradients of singular values, which are used to compute μ in special cases. The results are applied to analyze systems with simultaneous input and output perturbations, and the paper provides examples and computational experience to illustrate the effectiveness of the proposed methods. The key findings include the development of a function μ that can be used to analyze systems with structured uncertainties, and the demonstration that the function μ is related to the spectral radius and maximum singular value. The paper concludes that the proposed methods provide a more accurate and reliable analysis of multivariable feedback systems with structured uncertainties.