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010   $a3-319-91011-6
024 7 $a10.1007/978-3-319-91011-6
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035   $a(DE-He213)978-3-319-91011-6
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035   $a(PPN)229493769
035   $a(EXLCZ)994100000004831982
100   $a20180607d2019      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aInput-to-State Stability for PDEs /$fby Iasson Karafyllis, Miroslav Krstic
205   $a1st ed. 2019.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019.
215   $a1 online resource (XVI, 287 p. 1 illus. in color.) 
225 1 $aCommunications and Control Engineering,$x0178-5354
311   $a3-319-91010-8 
327   $aChapter 1. Preview -- Part I: ISS for First-Order Hyperbolic PDEs -- Chapter 2. Existence/Uniqueness Results for Hyperbolic PDEs -- Chapter 3. ISS in Spatial Lp Norms -- Part II. ISS for Parabolic PDEs -- Chapter 4. Existence/Uniqueness Results for Parabolic PDEs -- Chapter 5. ISS in Spatial L2 and H1 Norms -- Chapter 6. ISS in Spatial Lp Norms -- Part III. Small-Gain Analysis -- Chapter 7. Fading Memory Input-to-State Stability -- Chapter 8. PDE-ODE Loops -- Chapter 9. Hyperbolic PDE-PDE Loops -- Chapter 10. Parabolic PDE-PDE Loops -- Chapter 11. Parabolic-Hyperbolic PDE-PDE Loops -- Reference. .
330   $aThis book lays the foundation for the study of input-to-state stability (ISS) of partial differential equations (PDEs) predominantly of two classes?parabolic and hyperbolic. This foundation consists of new PDE-specific tools. In addition to developing ISS theorems, equipped with gain estimates with respect to external disturbances, the authors develop small-gain stability theorems for systems involving PDEs. A variety of system combinations are considered: PDEs (of either class) with static maps; PDEs (again, of either class) with ODEs; PDEs of the same class (parabolic with parabolic and hyperbolic with hyperbolic); and feedback loops of PDEs of different classes (parabolic with hyperbolic). In addition to stability results (including ISS), the text develops existence and uniqueness theory for all systems that are considered. Many of these results answer for the first time the existence and uniqueness problems for many problems that have dominated the PDE control literature of the last two decades, including?for PDEs that include non-local terms?backstepping control designs which result in non-local boundary conditions. Input-to-State Stability for PDEs will interest applied mathematicians and control specialists researching PDEs either as graduate students or full-time academics. It also contains a large number of applications that are at the core of many scientific disciplines and so will be of importance for researchers in physics, engineering, biology, social systems and others.
410  0$aCommunications and Control Engineering,$x0178-5354
606   $aControl engineering
606   $aPartial differential equations
606   $aElectrical engineering
606   $aSystem theory
606   $aControl and Systems Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/T19010
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
606   $aCommunications Engineering, Networks$3https://scigraph.springernature.com/ontologies/product-market-codes/T24035
606   $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070
615  0$aControl engineering.
615  0$aPartial differential equations.
615  0$aElectrical engineering.
615  0$aSystem theory.
615 14$aControl and Systems Theory.
615 24$aPartial Differential Equations.
615 24$aCommunications Engineering, Networks.
615 24$aSystems Theory, Control.
676   $a629.8
700   $aKarafyllis$b Iasson$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767164
702   $aKrstic$b Miroslav$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910483782403321
996   $aInput-to-State Stability for PDEs$92855553
997   $aUNINA