H∞ Optimal Estimation for Linear Coupled PDE Systems

Abstract

In this work, we present a Linear Matrix Inequality (LMI) based method to synthesize an optimal $mathcal{H}_{infty}$ estimator for a large class of linear coupled partial differential equations (PDEs) utilizing only finite dimensional measurements. Our approach extends the newly developed framework for representing and analyzing distributed parameter systems using operators on the space of square integrable functions that are equipped with multipliers and kernels of semi-separable class. We show that by redefining the state, the PDEs can be represented using operators that embed the boundary conditions and input-output relations explicitly. The optimal estimator synthesis problem is formulated as a convex optimization subject to LMIs that require no approximation or discretization.