{"product_id":"9783030081553","title":"Communications and Control Engineering","description":"\u003ch1\u003eCommunications and Control Engineering\u003c\/h1\u003e \u003ch2\u003eKarafyllis, Iasson; Krstic, Miroslav\u003c\/h2\u003e \u003cp\u003eThis 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. \u003c\/p\u003e\u003cp\u003eIn 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: \u003c\/p\u003e\n\n\u003cp\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003ePDEs (of either class) with static maps;\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003ePDEs (again, of either class) with ODEs;\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003ePDEs of the same class (parabolic with parabolic and hyperbolic with hyperbolic); and\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003efeedback loops of PDEs of different classes (parabolic with hyperbolic).\u003cbr\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003e\u003c\/p\u003e\n\n\n\n\n\n\n\nIn 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.\u003cp\u003e\u003c\/p\u003e\n\n\u003ci\u003eInput-to-State Stability for PDEs\u003c\/i\u003e 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. \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2019-01-10\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783030081553\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-319-91011-6\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 287\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":50090665312396,"sku":"9783030081553","price":152.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783030081553.jpg?v=1779505691","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783030081553","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}