English

Towards a comprehensive impossibility result for string stability

Optimization and Control 2018-10-29 v2

Abstract

We provide a comprehensive impossibility result towards achieving string stability, i.e. keeping local relative errors in check with local controllers independently of the size of a chain of subsystems. We significantly extend existing results, from the LTI setting to any homogeneous controllers that can be nonlinear, time-varying, and locally communicating. We prove this impossibility for a set of definitions with various norm choices, including the L2L_2-type which is more standard in the literature and a BIBO type criterion. All results hold for a general discrete-time controller which should cover most applications.

Keywords

Cite

@article{arxiv.1804.04858,
  title  = {Towards a comprehensive impossibility result for string stability},
  author = {Arash Farnam and Alain Sarlette},
  journal= {arXiv preprint arXiv:1804.04858},
  year   = {2018}
}
R2 v1 2026-06-23T01:22:40.542Z