On the exponential stability of an initial-boundary equation arising from strain feedback control of flexible robot arms with rigid offset

Abstract

This paper is concerned with an initial-boundary value equation arising from direct strain feedback control of flexible robot arms with a revolute joint and rigid offset. By analyzing the spectrum and by estimating the norm of the resolvent of the system operator associated with the equation, it is verified that the equation admits a unique solution and, furthermore, the solution is exponentially stable, no matter how long is the rigid offset.