The Interconnection Between Stability, D-Stability, µ-Values With Applications to Linear Systems

This study looks at how D-stability relates to the structured singular value for certain types of structured matrices, which helps us to understand dynamic systems influenced by structured and unstructured uncertainties. We share new results on D-stability, ensuring that eigenvalues remain in a specific area of the complex plane C even with permitted changes. The calculations of a singular value and a structured singular value are important measures to evaluate how well a system can handle changes, perform, and remain stable when faced with certain types of uncertainty. We establish a theoretical connection between these concepts by characterizing D stable regions within the µ-analysis framework. Numerical tests support our findings, showing how singular values and structured singular values behave with our method compared to traditional techniques.

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