Global Solvability of Time-Varying Semilinear Differential-Algebraic Equations, Boundedness and Stability of Their Solutions. II

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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. 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. © 2008 by World Scientific Publishing Co. Pte. Ltd. All Rights Reserved.
Notations.- Introduction.- Part I. Projector based approach.- 1 Linear constant coefficient DAEs.-.2 Linear DAEs with variable coefficients.- 3 Nonlinear DAEs.- Part II. Index-1 DAEs: Analysis and numerical treatment.- 4 Analysis.- 5 Numerical integration.- 6 Stability issues.- Part III. Computational aspects.- 7 Computational linear algebra aspects.- 8 Aspects of the numerical treatment of higher index DAEs.- Part IV. Advanced topics.- 9 Quasi-regular DAEs.- 10 Nonregular DAEs.- 11 Minimization with constraints described by DAEs.- 12 Abstract differential algebraic equations.- A. Linear Algebra - Basics.-.B. Technical Computations.- C Analysis.- References.- Index.
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