LEADER 05459nam 2200673Ia 450 001 9910453278503321 005 20200520144314.0 010 $a1-281-93401-1 010 $a9786611934019 010 $a981-279-181-7 035 $a(CKB)1000000000554866 035 $a(EBL)1193385 035 $a(SSID)ssj0000293986 035 $a(PQKBManifestationID)12086745 035 $a(PQKBTitleCode)TC0000293986 035 $a(PQKBWorkID)10303013 035 $a(PQKB)10881139 035 $a(MiAaPQ)EBC1193385 035 $a(WSP)00001947 035 $a(Au-PeEL)EBL1193385 035 $a(CaPaEBR)ebr10698817 035 $a(CaONFJC)MIL193401 035 $a(OCoLC)313650759 035 $a(EXLCZ)991000000000554866 100 $a20080222d2008 uy 0 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDifferential-algebraic systems$b[electronic resource] $eanalytical aspects and circuit applications /$fRicardo Riaza 210 $aSingapore ;$aHackensack, NJ $cWorld Scientific$d2008 215 $a1 online resource (344 p.) 300 $aDescription based upon print version of record. 311 $a981-279-180-9 320 $aIncludes bibliography (p. 309-324) and index. 327 $aPreface; Contents; 1. Introduction; 1.1 Historical remarks: Different origins, different names; 1.2 DAE analysis; 1.2.1 Indices; 1.2.2 Dynamics and singularities; 1.2.3 Numerical aspects; 1.3 State vs. semistate modeling; 1.4 Formulations; 1.4.1 Input-output descriptions; 1.4.2 Leading terms; 1.4.3 Semiexplicit, semilinear and quasilinear DAEs; 1.4.3.1 Semiexplicit and semilinear DAEs; 1.4.3.2 Hessenberg DAEs; 1.4.3.3 Quasilinear DAEs; 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 327 $a2.1.1 Matrix pencils and the Kronecker canonical form 2.1.2 Solving linear time-invariant DAEs via the KCF; 2.1.3 A glance at projector-based techniques; 2.1.3.1 Index one characterization via projectors; 2.1.3.2 Decoupling of linear time-invariant index one DAEs; 2.1.3.3 Geometrical remarks; 2.1.3.4 Higher index problems; 2.1.3.5 Some auxiliary properties of the projectors Pi and Qi; 2.2 Properly stated linear time-varying DAEs; 2.2.1 On standard form index one problems; 2.2.2 Properly stated leading terms; 2.2.3 P-projectors: Matrix chain and the tractability index; 2.2.3.1 Matrix chain 327 $a2.2.3.2 The tractability index of regular linear DAEs 2.2.4 The ?-framework; 2.2.4.1 Alternative chain construction; 2.2.4.2 Equivalence of the P- and ?-chains; 2.2.4.3 Some properties of the projectors ?i and Mi; 2.2.5 Decoupling; 2.2.6 A tutorial example; 2.2.6.1 Index one; 2.2.6.2 Index two; 2.2.6.3 Index three; 2.2.7 Regular points; 2.3 Standard formlinear DAEs; 2.3.1 The tractability index of standard form DAEs; 2.3.2 Decoupling; 2.3.3 Time-invariant problems revisited; 2.4 Other approaches for linear DAEs: Reduction techniques; 3. Nonlinear DAEs and reduction methods 327 $a3.1 Semiexplicit index one DAEs 3.2 Hessenberg systems; 3.3 Some notions from differential geometry; 3.4 Quasilinear DAEs: The geometric index; 3.4.1 The framework of Rabier and Rheinboldt; 3.4.2 Index zero and index one points; 3.4.2.1 Index zero points; 3.4.2.2 Index one points; 3.4.3 Higher index points; 3.4.3.1 Index two points; 3.4.3.2 Index ? points; 3.4.4 Manifold sequences and locally regular DAEs; 3.4.4.1 Regular manifold, solution manifold, and locally regular DAEs; 3.4.4.2 Manifold sequences within different reduction approaches; 3.4.5 Local equivalence 327 $a3.4.5.1 The index: Independence of reduction pairs and invariance 3.4.5.2 C-conjugacy of state space descriptions; 3.4.5.3 On the link between local equivalence and reduction operators; 3.4.6 Examples; 3.4.6.1 Semiexplicit index one DAEs; 3.4.6.2 Hessenberg DAEs; 3.4.6.3 A locally regular DAE with di.erent indices; 3.4.7 Nonautonomous problems; 3.4.7.1 Geometric index and reduction in the nonautonomous context; 3.4.7.2 Semiexplicit index one DAEs; 3.4.7.3 Nonautonomous Hessenberg DAEs; 3.4.7.4 Schur reduction and semiexplicit DAEs; 3.5 Dynamical aspects 327 $a3.6 Reduction methods for fully nonlinear DAEs 330 $aDifferential-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 resul 606 $aDifferential-algebraic equations 606 $aElectric circuits$xMathematical models 608 $aElectronic books. 615 0$aDifferential-algebraic equations. 615 0$aElectric circuits$xMathematical models. 676 $a512.56 676 $a512/.56 676 $a621.3815 700 $aRiaza$b Ricardo$0966455 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910453278503321 996 $aDifferential-algebraic systems$92193384 997 $aUNINA