Riesz Bases in Control Theory

Abstract

In this paper we examine the reachable states of motion of a vibrating string, starting from given initial and boundary conditions and driving the string by an appropriate u(t) control force which is an element of a specified function field. The motion is described using Fourier methodology. The convergence of the series expansion is examined for different function classes. This requires spectral-theoretical studies to become acquainted with the asymptotic behaviour of the eigenfunctions and eigenvalues.