Boundary Exponential Stabilization of 1-Dimensional Inhomogeneous Quasi-Linear Hyperbolic Systems

Long Hu (1) , Rafael Vazquez (2) , Florent Di Meglio , Miroslav Krstic (3)

1 Shandong University
2 Universidad de Sevilla = University of Seville
3 MAE - UC San Diego - Department of Mechanical and Aerospace Engineering [Univ California San Diego]

This paper deals with the problem of boundary stabilization of first-order $n\times n$ inhomogeneous quasi-linear hyperbolic systems. A backstepping method is developed. The main result supplements the previous works on how to design multiboundary feedback controllers to achieve exponential stability with arbitrary decay rate of the original nonlinear system in the spatial $H^2$ sense.

Domaines: Automatique / Robotique

Long Hu, Rafael Vazquez, Florent Di Meglio, Miroslav Krstic. Boundary Exponential Stabilization of 1-Dimensional Inhomogeneous Quasi-Linear Hyperbolic Systems. SIAM Journal on Control and Optimization, 2019, 57 (2), pp.963-998. ⟨10.1137/15M1012712⟩. ⟨hal-02437227⟩