| Description |
1 online resource (xiv, 330 pages) : illustrations |
| Contents |
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 |
| Summary |
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. Beginning with elementary aspects, the author succeeds in providing a self-contained and comprehensive presentation of several advanced topics in DAE theory, such as the full characterization of linear time-varying equations via projector methods or the geometric reduction of nonlinear systems. Recent results on singularities are extensively discussed. The book also addresses in detail differential-algebraic models of electrical and electronic circuits, including index characterizations and qualitative aspects of circuit dynamics. In particular, the reader will find a thorough discussion of the state/semistate dichotomy in circuit modeling. The state formulation problem, which has attracted much attention in the engineering literature, is cleverly tackled here as a reduction problem on semistate models |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
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Print version record |
| Subject |
Differential-algebraic equations.
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Electric circuits -- Mathematical models
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MATHEMATICS -- Algebra -- Linear.
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Differential-algebraic equations
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Electric circuits -- Mathematical models
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| Form |
Electronic book
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| ISBN |
9812791817 |
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9789812791818 |
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1281934011 |
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9781281934017 |
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9786611934019 |
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6611934014 |
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