We present a class of spatially interconnected systems with boundary conditions that have close links with their spatially invariant extensions. In particular well-posedness, stability and performance of the extension imply the same characteristics for the actual, finite extent system. In turn existing synthesis methods for control of spatially invariant systems can be extended to this class. The relation between the two kinds of system is proved using ideas based on the 'Method of Images' of partial differential equations theory and uses symmetry properties of the interconnection as a key tool.
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Langbort et al. (2004) studied this question.
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