Complexity reduction through a Schur-based decomposition for reachability analysis of linear time-invariant systems

@article{Kaynama2011ComplexityRT,
  title={Complexity reduction through a Schur-based decomposition for reachability analysis of linear time-invariant systems},
  author={Shahab Kaynama and Meeko Oishi},
  journal={International Journal of Control},
  year={2011},
  volume={84},
  pages={165 - 179}
}
This article presents a method for complexity reduction in reachability analysis and safety-preserving controller synthesis via Schur-based decomposition. The decomposition results in either decoupled or weakly-coupled (lower dimensional) subsystems. Reachable sets, computed independently for each subsystem, are back-projected and intersected to yield an overapproximation of the actual reachable set. Moreover, applying this technique to a class of unstable LTI systems, we show that when certain… 
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