Solution to the Algebraic Riccati Equation for Parabolic Systems.

This paper presents an analytical solution to the operator algebraic Riccati equation ARE for selfadjoint parabolic systems. The solution to the operator ARE is important in the design of the steady state, on line filter for estimating the systems states. This analytical solution is derived by considering the operator analog of Potters method of using the Hamiltonian systems eigenvectors and eigenvalues to solve a finite dimensional ARE. As an example of using this analytical solution, the steady state filtering error covariance for the 2D heat equation is studied.