A note on computing system radii for Galerkin approximations of elastic systems

Abstract

Finite element and other Galerkin approximations often used to construct finite dimensional systems for control design are discussed. These methods produce systems with very special structure and this structure can be exploited in developing computational algorithms. A considerable portion of numerical linear algebra is devoted to numerical methods for systems involving banded, sparse, or block diagonal matrices. However, most numerical algorithms currently used in control design do not take advantage of the special structure that results from approximating infinite dimensional systems by Galerkin models. The authors discuss the problem of computing system radii (e.g., controllability, stabilizability, observability, and detectability margins) for finite element approximations of elastic systems. The simple one dimensional wave equation is used to illustrate the basic ideas.<>