Convergence of approximations in feedback control of structures

Convergence of linear quadratic regulator (LQR) problems in structures is discussed. The abstract formulation of the system using a variational framework based on sesquilinear forms is considered. Since convergence theorems require uniform stabilizability of the finite-dimensional approximating system, we present a detailed proof of a fundamental lemma due to Banks and Ito [1] which can be used to easily verify this condition for many applications. Existing results for the well posedness of the infinite-dimensional system and convergence of Galerkin approximations are summarized.