On stability of nonlinear hyperbolic systems with reaction and switching

Author

Hao Yang ; Bin Jiang ; Cocquempot, V. ; Aitouche, A.

Author_Institution

Coll. of Autom. Eng. (CAE), Nanjing Univ. of Aeronaut. & Astronaut., Nanjing, China

fYear

2013

fDate

17-19 June 2013

Firstpage

59

Lastpage

64

Abstract

This paper investigates the exponential stability in L² norm of scalar nonlinear hyperbolic systems of balance laws with the reaction that may be accumulative or dissipative. Two Lyapunov-based stability criteria that depend on the system parameters and boundary data are proposed with fully considering the reactions´ characteristics. The new results can help to construct a common Lyaunov function to stabilize the switched nonlinear hyperbolic systems under arbitrary switching. Several traffic system examples are taken to illustrate the theoretical results.

Keywords

Lyapunov methods; asymptotic stability; hyperbolic equations; nonlinear systems; partial differential equations; stability criteria; time-varying systems; L² norm; Lyapunov-based stability criteria; Lyaunov function; balance laws; boundary data; exponential stability; nonlinear hyperbolic system stability; reaction characteristics; scalar nonlinear hyperbolic systems; switched nonlinear hyperbolic systems; system parameters; traffic system; Boundary conditions; Lyapunov methods; Stability criteria; Switched systems; Switches; Vehicles; Boundary control; Nonlinear hyperbolic partial differential equation; Stability; Switched systems;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference (ACC), 2013

Conference_Location

Washington, DC

ISSN

0743-1619

Print_ISBN

978-1-4799-0177-7

Type

conf

DOI

10.1109/ACC.2013.6579814

Filename

6579814