rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Stability and Boundary Stabilization of 1-D Hyperbolic Systems
  name:
    name part: Bastin, Georges.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Coron, Jean-Michel.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2016
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIV, 307 p. 61 illus., 31 illus. in color. online resource.
  abstract: This 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.
  table of contents: Hyperbolic 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.
  note: by Georges Bastin, Jean-Michel Coron.
  subject:
    topic: Mathematics
  subject:
    topic: Dynamics
  subject:
    topic: Ergodic theory
  subject:
    topic: Partial differential equations
  subject:
    topic: System theory
  subject:
    topic: Mathematical physics
  subject:
    topic: Vibration
  subject:
    topic: Dynamical systems
  subject:
    topic: Mathematics
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Dynamical Systems and Ergodic Theory
  subject:
    topic: Systems Theory, Control
  subject:
    topic: Mathematical Applications in the Physical Sciences
  subject:
    topic: Vibration, Dynamical Systems, Control
  classification: QA370-380
  classification: 515.353
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Progress in Nonlinear Differential Equations and Their Applications, 88
  identifier: 9783319320625
  identifier: http://dx.doi.org/10.1007/978-3-319-32062-5
  record info:
    record creation date: 160726
    record change date: 20160726151515.0
    record identifier: 978-3-319-32062-5