A comparison between LQR control for a long string of SISO systems and LQR control of the infinite spatially invariant version

In this paper we consider a long string of SISO systems which in the limit becomes a scalar infinite spatially invariant system. We compare the LQR control for long-but-finite strings with the LQR control for the corresponding infinite strings. We give analytical and numerical examples where these are quite different and we investigate the cause. In addition, we obtain sufficient conditions for the LQR solutions to be similar as the length of the string increases.