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 -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}
}