Stability and Boundary Stabilization of 1-D Hyperbolic Systems. 1st ed. 2016

種類:

電子ブック

責任表示:

by Georges Bastin, Jean-Michel Coron

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2016

著者名:

• Bastin, Georges.
• Coron, Jean-Michel.
• SpringerLink (Online service)

シリーズ名:

PNLDE Subseries in Control ; 88

ISBN:

9783319320625 [3319320629]    

注記:

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.
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

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