A limiting property of the matrix exponential with application to multi-loop control

@article{Trimpe2009ALP,
  title={A limiting property of the matrix exponential with application to multi-loop control},
  author={Sebastian Trimpe and Raffaello D'Andrea},
  journal={Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference},
  year={2009},
  pages={6419-6425}
}
A limiting property of the matrix exponential is proven: For a real square matrix, where the log norm of the upper-left n by n block approaches negative infinity in a limiting process, the matrix exponential goes to zero in the first n rows and n columns. This property is useful for simplification of dynamic systems that exhibit modes with sufficiently different time scales; for example, in multi-loop control systems with fast inner and slow outer feedback loops. For this case, we derive a time… CONTINUE READING