Toward a Comprehensive Theory for Stability Regions of a Class of Nonlinear Discrete Dynamical Systems

Autor(es)

Dias, Elaine Santos ^{[1, 2]} ; Costa Alberto, Luis Fernando ^[1] ; Amaral, Fabiolo Moraes ^[3] ; Chiang, Hsiao-Dong ^[4]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Sao Carlos Sch Engn, Dept Elect & Comp Engn, BR-13566590 Sao Paulo - Brazil

^[2] UFSB Fed Univ Southern Bahia, BR-45613204 Porto Seguro - Brazil

^[3] IFBA Fed Inst Educ Bahia, BR-40301015 Salvador, BA - Brazil

^[4] Cornell Univ, Sch Elect & Comp Engn, Ithaca, NY 14853 - USA

• Tipo de documento: Artigo Científico
• Fonte: IEEE Transactions on Automatic Control; v. 66, n. 9, p. 4371-4377, SEP 2021.
• Citações Web of Science: 0

Resumo

A comprehensive theory for the stability boundaries and the stability regions of a general class of nonlinear discrete dynamical systems is developed in this article. This general class of systems is modeled by diffeomorphisms and admits as limit sets only fixed points and periodic orbits. Topological and dynamical characterizations of stability boundaries are developed. Necessary and sufficient conditions for fixed points and periodic orbits to lie on the stability boundary are derived. Numerical examples, including applications to associative neural networks illustrating the theoretical developments, are presented. (AU)

• Processo FAPESP: 14/14141-8 - Estudo da região de estabilidade de sistemas dinâmicos discretos
• Beneficiário: Elaine Santos Dias
• Modalidade de apoio: Bolsas no Brasil - Mestrado
• Processo FAPESP: 14/50851-0 - INCT 2014: Instituto Nacional de Ciência e Tecnologia para Sistemas Autônomos Cooperativos Aplicados em Segurança e Meio Ambiente
• Beneficiário: Marco Henrique Terra
• Modalidade de apoio: Auxílio à Pesquisa - Temático