Backstepping boundary stabilization and state estimation of a 2 × 2 linear hyperbolic system

By Rafael Vazquez, Miroslav Krstic, Jean-Michel Coron. IEEE Conference on Decision and Control and European Control Conference, 2011

304 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Stability and Boundary Stabilization of 1-D Hyperbolic Systems (2016, background): “24) is established in Vazquez et al. (2011). The exponential stability of the error system (7.”
Control of a 2 × 2 coupled linear hyperbolic system sandwiched between 2 ODEs (2018, methodology): “In the closed-loop system including the plant (1)-(4), (153), (154) and the controller U(t) (177), there exist positive constants λm and Υ0m making that |U(t)| is bounded and exponentially convergent to zero in the sense of |U(t)| ≤ Υ0me λm 2 t.”
Stabilization of a System of $n+1$ Coupled First-Order Hyperbolic Linear PDEs With a Single Boundary Input (2013, methodology): “In this paper, we propose to extend the control design of [37] to a broader class of systems.”
Local exponential H2 stabilization of a 2 × 2 quasilinear hyperbolic system using backstepping (2011, methodology): “[22] M. Krstic, A. Krupadanam, and C. Jacobson, Self-Tuning Control of a Nonlinear Model of Combustion Instabilities, IEEE Transactions on Control Systems Technology, 7 (1999), pp. 424–435 [23] M. Krstic and A. Smyshlyaev, Backstepping boundary control for first order hyperbolic PDEs and application”