Differential-algebraic systems : analytical aspects and circuit applications /

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Differential-algebraic equations (DAEs) provide an essential tool for system modeling and analysis within different fields of applied sciences and engineering. This book addresses modeling issues and analytical properties of DAEs, together with some applications in electrical circuit theory. Beginni...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Riaza, Ricardo
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Singapore, SG : World Scientific, ©2008.
Temas:
Differential-algebraic equations.
Electric circuits > Mathematical models.
Équations différentielles algébriques.
Circuits électriques > Modèles mathématiques.
MATHEMATICS > Algebra > Linear.
Differential-algebraic equations
Electric circuits > Mathematical models
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 1. Introduction. 1.1. Historical remarks: different origins, different names. 1.2. DAE analysis. 1.3. State vs. semistate modeling. 1.4. Formulations. 1.5. Contents and structure of the book
  • Analytical aspects of DAEs. 2. Linear DAEs and projector-based methods. 2.1. Linear time-invariant DAEs. 2.2. Properly stated linear time-varying DAEs. 2.3. Standard form linear DAEs. 2.4. Other approaches for linear DAEs: reduction techniques. 3. Nonlinear DAEs and reduction methods. 3.1. Semiexplicit index one DAEs. 3.2. Hessenberg systems. 3.3. Some notions from differential geometry. 3.4. Quasilinear DAEs: the geometric index. 3.5. Dynamical aspects. 3.6. Reduction methods for fully nonlinear DAEs. 3.7. The differentiation index and derivative arrays. 4. Singularities. 4.1. What is a singular DAE? 4.2. Singularities of properly stated linear time-varying DAEs. 4.3. Singularities of standard form linear time-varying DAEs. 4.4. Singularities of autonomous quasilinear DAEs
  • Semistate models of electrical circuits. 5. Nodal analysis. 5.1. Background on graphs and electrical circuits. 5.2. Formulation of nodal models. 5.3. Index analysis: fundamentals. 5.4. Index analysis: passive circuits. 5.5. Index analysis: tree methods for non-passive circuits. 6. Branch-oriented methods. 6.1. Branch-oriented semistate models. 6.2. Geometric index analysis and reduction of branch models. Qualitative properties.

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