Differential-Algebraic Systems: Analytical Aspects and Circuit ApplicationsDifferential-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. |
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Differential-algebraic Systems: Analytical Aspects and Circuit Applications Ricardo Riaza Limited preview - 2008 |
Differential-algebraic Systems: Analytical Aspects And Circuit Applications Ricardo Riaza Limited preview - 2008 |
Common terms and phrases
actually Additionally algebraic allowed analysis apply approach arising assume assumption branch called capacitance capacitors Chapter characterization choice circuit Comput condition connected considered constant construction context controlled corresponding defined Definition depicted derivative detailed different differential differential-algebraic discussed displayed dynamic equations equivalent example existence explicit expression fact follows formulation framework given holds identity implicit implies independent inductors leading Lemma linear locally loop manifold mapping Math matrix means methods models nodal nonlinear nonsingular Note notion numerical original particular passive pencil points positive possible present problems projector proof properties Proposition quasilinear DAEs rank reader reads reduction referred regular relation Remark requirement resistors respectively singular singular points smooth solution sources space structure subsection supporting Theorem theory tractability index tree variables voltage whereas yields