Interconnections between µ-Value and D-Stable, D(a)-Stable Matrices from Economic Models

[EN] In this paper, we review a number of well established methods to study the interconnection between D-stability and µ-values. The D-stability in economic, and dynamic systems plays a crucial role for maintaining equilibrium under proportional changes in parameters, for instance, prices, producti...

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Detalles Bibliográficos
Autores: Rehman, Mutti-Ur, Akram, Saima, Farxod, Ixtiyarov, Ochilov, Narzillo, Shahlokhon, Gafurova, Fuzaylova-Khakimovna, Nigina, Tukhtayev, Umidjon, Atoeva, Makhliyo
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:dnet:riunet______::d96291a69c1c43d60e656615ef0afa91
Acceso en línea:https://riunet.upv.es/handle/10251/233843
Access Level:acceso abierto
Palabra clave:D(a)-stable matrices
D-stable matrices
Economic models
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Descripción
Sumario:[EN] In this paper, we review a number of well established methods to study the interconnection between D-stability and µ-values. The D-stability in economic, and dynamic systems plays a crucial role for maintaining equilibrium under proportional changes in parameters, for instance, prices, production levels, or financial flows. The computation of structured singular value a.k.a µ-value is a well-known mathematical tool for analysis of systems appearing in robust control. The µ-value provides the quantitative measure of linear systems stability subject to structured uncertainties. The approximation of an upper bounds of µ-value plays a critical role for ensuring robust stability and performance which guarantees in practical linear control systems. This article also presents the state-of-the-art mathematical methods for approximating upper bounds of µ-values. The µ-value is deeply interconnected with D-stability theory of economic models. The key methods includes the computation of upper bounds of µ-values for mixed real and complex uncertainties, optimization based methods, linear matrix inequalities (LMI)-based techniques.