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2013 American Control Conference
This article investigates the problem of estimating the state of discretized hyperbolic scalar partial differential equations. It uses a Godunov scheme to discretize the socalled Lighthill-Whitham-Richards equation with a triangular flux function, and proves that the resulting nonlinear dynamical system can be decomposed in a piecewise affine manner. Using this explicit representation, the system is written as a switching dynamical system (hybrid system), with an exponential number of modes.doi:10.1109/acc.2013.6580198 fatcat:4hkve7p7oveyhgjvuh3p6aokye