Extends PIE representation inductively to multivariate PDEs via domain intersections, proves consistency condition for operator inverse, and enables SDP-based stability analysis with PIETOOLS software.
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A single boundary controller for the LWR traffic model is not certified by the main theorems, because the proof omits endpoint optima and mishandles infeasibility of the stability constraint.
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A State-Space Representation of Coupled Linear Multivariate PDEs and Stability Analysis using SDP
Extends PIE representation inductively to multivariate PDEs via domain intersections, proves consistency condition for operator inverse, and enables SDP-based stability analysis with PIETOOLS software.