04441nam 22005895 450 991048378240332120200704022711.03-319-91011-610.1007/978-3-319-91011-6(CKB)4100000004831982(DE-He213)978-3-319-91011-6(MiAaPQ)EBC5419692(PPN)229493769(EXLCZ)99410000000483198220180607d2019 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierInput-to-State Stability for PDEs /by Iasson Karafyllis, Miroslav Krstic1st ed. 2019.Cham :Springer International Publishing :Imprint: Springer,2019.1 online resource (XVI, 287 p. 1 illus. in color.) Communications and Control Engineering,0178-53543-319-91010-8 Chapter 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. .This 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.Communications and Control Engineering,0178-5354Control engineeringPartial differential equationsElectrical engineeringSystem theoryControl and Systems Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/T19010Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Communications Engineering, Networkshttps://scigraph.springernature.com/ontologies/product-market-codes/T24035Systems Theory, Controlhttps://scigraph.springernature.com/ontologies/product-market-codes/M13070Control engineering.Partial differential equations.Electrical engineering.System theory.Control and Systems Theory.Partial Differential Equations.Communications Engineering, Networks.Systems Theory, Control.629.8Karafyllis Iassonauthttp://id.loc.gov/vocabulary/relators/aut767164Krstic Miroslavauthttp://id.loc.gov/vocabulary/relators/autBOOK9910483782403321Input-to-State Stability for PDEs2855553UNINA