$H_{\infty}$-Optimal Estimator Synthesis for Coupled Linear 2D PDEs using Convex Optimization

Any suitably well-posed PDE in two spatial dimensions can be represented as a Partial Integral Equation (PIE) -- with system dynamics parameterized using Partial Integral (PI) operators. Furthermore, $L_2$-gain analysis of PDEs with a PIE representation can be posed as a linear operator inequality,