LEADER 04199nam 22006855 450 001 996466639503316 005 20200703072240.0 010 $a3-540-45543-4 024 7 $a10.1007/82934 035 $a(CKB)1000000000233224 035 $a(SSID)ssj0000324441 035 $a(PQKBManifestationID)11912682 035 $a(PQKBTitleCode)TC0000324441 035 $a(PQKBWorkID)10313416 035 $a(PQKB)11015149 035 $a(DE-He213)978-3-540-45543-1 035 $a(MiAaPQ)EBC6285389 035 $a(MiAaPQ)EBC5578428 035 $a(Au-PeEL)EBL5578428 035 $a(OCoLC)1066185940 035 $a(PPN)155218247 035 $a(EXLCZ)991000000000233224 100 $a20121227d2002 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aLinear Delay-Differential Systems with Commensurate Delays: An Algebraic Approach$b[electronic resource] /$fby Heide Gluesing-Luerssen 205 $a1st ed. 2002. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2002. 215 $a1 online resource (X, 178 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1770 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-42821-6 320 $aIncludes bibliographical references (pages [169]-174) and index. 327 $aIntroduction -- The Algebraic Framework -- The Algebraic Structure of H_0. Divisibility Properties. Matrices over H_0. Systems over Rings: A Brief Survery. The Nonfinitely Generated Ideals of H_0. The Ring H as a Convolution Algebra. Computing the Bezout Identity -- Behaviors of Delay-Differential Systems. The Lattice of Behaviors. Input/Output Systems. Transfer Classes and Controllable Systems. Subbehaviors and Interconnections. Assigning the Characteristic Function. Biduals of Nonfinitely Generated Ideals -- First-Order Representations. Multi-Operator Systems. The Realization Procedure of Fuhrmann. First-Order Realizations. Some Minimality Issues. 330 $aThe book deals with linear time-invariant delay-differential equations with commensurated point delays in a control-theoretic context. The aim is to show that with a suitable algebraic setting a behavioral theory for dynamical systems described by such equations can be developed. The central object is an operator algebra which turns out to be an elementary divisor domain and thus provides the main tool for investigating the corresponding matrix equations. The book also reports the results obtained so far for delay-differential systems with noncommensurate delays. Moreover, whenever possible it points out similarities and differences to the behavioral theory of multidimensional systems, which is based on a great deal of algebraic structure itself. The presentation is introductory and self-contained. It should also be accessible to readers with no background in delay-differential equations or behavioral systems theory. The text should interest researchers and graduate students. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1770 606 $aCalculus of variations 606 $aAlgebra 606 $aDifferential equations 606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 615 0$aCalculus of variations. 615 0$aAlgebra. 615 0$aDifferential equations. 615 14$aCalculus of Variations and Optimal Control; Optimization. 615 24$aAlgebra. 615 24$aOrdinary Differential Equations. 676 $a515.35 700 $aGluesing-Luerssen$b Heide$4aut$4http://id.loc.gov/vocabulary/relators/aut$066356 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466639503316 996 $aLinear delay-differential systems with commensurate delays: an algebraic approach$91907518 997 $aUNISA