Distributed Control: A Sequentially Semi-Separable Approach for Spatially Heterogeneous Linear Systems

We consider the problem of designing controllers for spatially-varying interconnected systems distributed in one spatial dimension. The matrix structure of such systems can be exploited to allow fast analysis and design of centralized controllers with simple distributed implementations. Iterative algorithms are provided for stability analysis,
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analysis and sub-optimal controller synthesis. For practical implementation of the algorithms, approximations can be used, and the computational efficiency and accuracy are demonstrated on an example.