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In the distant-downstream control of irrigation channels, the interactions between pools and the internal time-delay for water to travel from upstream to downstream, impose limitations on global performance, i.e., there exists propagation of water-level errors and amplification of flows over gates in the upstream direction. This brief analyzes these coupling properties for a string of identical pools, both with identical feedback controllers and with non-identical feedback controllers. A definition of string stability in terms of bounded water-level errors and bounded flows is given. It is shown that for a string of an infinite number of pools, string stability cannot be achieved by decentralized distant-downstream feedback control mainly due to the internal time-delay for water to travel from upstream to downstream. Applying the analysis results on string stability to a string of a finite number of pools, i.e., using non-identical feedback controllers in a distant-downstream control structure such that the closed-loop bandwidths of the subsystems increase from downstream to upstream, a much better global performance can be achieved than in the case of using identical feedback controllers.