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This article investigates the problem of estimating the state of discretized hyperbolic scalar partial differential equations. It uses a Godunov scheme to discretize the so-called 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, with a state space partitioned into an exponentialdoi:10.1109/tac.2014.2342151 fatcat:pnp6fzrv4nax3prnqkzie4vnim