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010   $a3-319-32062-9
024 7 $a10.1007/978-3-319-32062-5
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035   $a(DE-He213)978-3-319-32062-5
035   $a(MiAaPQ)EBC4613335
035   $a(PPN)194515370
035   $a(EXLCZ)993710000000765126
100   $a20160726d2016      u|         0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aStability and boundary stabilization of 1-D hyperbolic systems /$fby Georges Bastin, Jean-Michel Coron
205   $a1st ed. 2016.
210  1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2016.
215   $a1 online resource (XIV, 307 p. 61 illus., 31 illus. in color.)
225 1 $aPNLDE Subseries in Control ;$v88
311   $a3-319-32060-2 
320   $aIncludes bibliographical references and index.
327   $aHyperbolic Systems of Balance Laws -- Systems of Two Linear Conservation Laws -- Systems of Linear Conservation Laws -- Systems of Nonlinear Conservation Laws -- Systems of Linear Balance Laws -- Quasi-Linear Hyperbolic Systems -- Backstepping Control -- Case Study: Control of Navigable Rivers -- Appendices -- References -- Index.
330   $aThis monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts in whichever setting is most familiar to them. With these examples, it also illustrates how control boundary conditions may be defined for the most commonly used control devices. The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching. They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis. Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones. They go on to show how the problem of boundary stabilization of systems of two balance laws by both full-state and dynamic output feedback in observer-controller form is solved by using a ?backstepping? method, in which the gains of the feedback laws are solutions of an associated system of linear hyperbolic PDEs. The final chapter presents a case study on the control of navigable rivers to emphasize the main technological features that may occur in practical applications of boundary feedback control. Stability and Boundary Stabilization of 1-D Hyperbolic Systems will be of interest to graduate students and researchers in applied mathematics and control engineering. The wide range of applications it discusses will help it to have as broad an appeal within these groups as possible.
410  0$aPNLDE Subseries in Control ;$v88
606   $aDifferential equations, Partial
606   $aDynamics
606   $aErgodic theory
606   $aSystem theory
606   $aMathematical physics
606   $aVibration
606   $aDynamics
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
606   $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X
606   $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070
606   $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120
606   $aVibration, Dynamical Systems, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/T15036
615  0$aDifferential equations, Partial.
615  0$aDynamics.
615  0$aErgodic theory.
615  0$aSystem theory.
615  0$aMathematical physics.
615  0$aVibration.
615  0$aDynamics.
615 14$aPartial Differential Equations.
615 24$aDynamical Systems and Ergodic Theory.
615 24$aSystems Theory, Control.
615 24$aMathematical Applications in the Physical Sciences.
615 24$aVibration, Dynamical Systems, Control.
676   $a515.353
700   $aBastin$b G$g(Georges),$f1947-$4aut$4http://id.loc.gov/vocabulary/relators/aut$0128468
702   $aCoron$b Jean-Michel$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910254064503321
996   $aStability and Boundary Stabilization of 1-D Hyperbolic Systems$91964446
997   $aUNINA