Local exponential H2 stabilization of a 2 × 2 quasilinear hyperbolic system using backstepping

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

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Control of Homodirectional and General Heterodirectional Linear Coupled Hyperbolic PDEs (2015, methodology): “This degree of freedom in the control design has never appeared in previous backstepping designs for hyperbolic systems [8], [13].”
Null Controllability and Finite Time Stabilization for the Heat Equations with Variable Coefficients in Space in One Dimension via Backstepping Approach (2017, methodology): “Since then, this has been applied to study the stability of parabolic equations in [33,34], of hyperbolic systems in [9,10,17,18,22], of nonlinear parabolic equations in [36], of Korteweg–de Vries equations in [4] and of Kuramoto–Sivashinsky equations in [28].”
Backstepping boundary stabilization and state estimation of a 2 × 2 linear hyperbolic system (2011, methodology): “The method can also be applied if the system is not linear but quasilinear, obtaining a local result; the details can be found in [22].”
Stabilization of a System of $n+1$ Coupled First-Order Hyperbolic Linear PDEs With a Single Boundary Input (2013, background): “In [11] and [38] control laws for a system of two coupled nonlinear PDEs are derived, whereas in [7], [10], [21], [30], [31] sufficient conditions for exponential stability are given for various classes of quasilinear first-order hyperbolic systems.”