A comparison between LQR control for a long string of 2 × 2 MIMO systems and LQR control of the infinite spatially invariant version

We compare the LQR control for a long-but-finite string of 2 × 2 MIMO systems with the LQR control for the corresponding infinite-dimensional spatially invariant system. We provide analytical and numerical examples where these are different and we investigate the cause. We also provide sufficient conditions for the LQR solutions to be similar as the length of the string increases. This work extends to the 2 × 2 MIMO systems part of the analysis presented in recent papers for the scalar case.