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.
Proof For the case n = 1, the result follows by inspection
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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.