Stabilization of a System of $n+1$ Coupled First-Order Hyperbolic Linear PDEs With a Single Boundary Input

By Florent Di Meglio, Rafael Vazquez, Miroslav Krstic. IEEE Transactions on Automatic Control, 2013

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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].”
Boundary exponential stabilization of 1-D inhomogeneous quasilinear hyperbolic systems (2015, methodology): “8), we use the following Volterra transformation of the second kind, which is similar to the one in [8] and [9]: γ(t, x) = w(t, x) − ∫ x”