Exponential Stability and Transfer Functions of Processes Governed by Symmetric Hyperbolic Systems

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Control of Homodirectional and General Heterodirectional Linear Coupled Hyperbolic PDEs (2015, background): “Introduction a) Background: Coupled first-order linear hyperbolic systems, typically formulated on a 1-D spatial domain normalized to the interval (0, 1), are common in modeling of traffic flow [2], heat exchangers [31], open channel flow [7], [10] or multiphase flow [11], [15], [16].”
Review on computational methods for Lyapunov functions (2015, methodology): “Some references, where Lyapunov functions are used to study the stability of PDEs are Xu and Sallet 2002 [226], Coron, d’Andrea-Novel, and Bastin 2007 [61], and Prieur and Mazenc 2012 [194].”
A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws (2004, background): “With a view to the boundary control design, the following candidate Lyapunov function is introduced (see also [8]) :”
Using hyperbolic systems of balance laws for modeling, control and stability analysis of physical networks (2009, methodology): “It is also similar to the Lyapunov function used in [19] to analyse the stability of a general class of linear symmetric hyperbolic systems.”