A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws

By Jean-Michel Coron, Brigitte d'Andréa-Novel, G. Bastin. IEEE Conference on Decision and Control, 2004

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Strict Lyapunov functions for semilinear parabolic partial differential equations (2011, background): “It requires to demonstrate a precompactness property for the solutions, which may be difficult to prove (and is not even always satisfied, as illustrated by the hyperbolic systems considered in [6]).”
Using hyperbolic systems of balance laws for modeling, control and stability analysis of physical networks (2009, methodology): “The contribution of [7] was to show how this kind of Lyapunov function can be extended to the form (34) in order to prove the exponential convergence of nonlinear systems of conservation laws in H(2)(0, L)-norm.”
Review on computational methods for Lyapunov functions (2015, background): “Filippov 1988 [76], the asymptotic stability of the origin for the continuous-time switched system under arbitrary switching”
Boundary exponential stabilization of 1-D inhomogeneous quasilinear hyperbolic systems (2015, background): “[6] Jean-Michel Coron, Brigitte d’Andréa Novel, and Georges Bastin.”
Backstepping boundary stabilization and state estimation of a 2 × 2 linear hyperbolic system (2011, methodology): “More recently, an approach using control Lyapunov functions has been developed, for 2× 2 quasilinear systems [2] and n × n quasilinear systems [3].”