Towards tight impossibility and possibility results for string stability
Arash Farnam, Alain Sarlette · arXiv (Cornell University) · 2018
We provide two complementary results that clarify the issue of string stability, i.e. keeping local errors in check with local controllers independently of the size of a chain of subsystems. First, we significantly extend the impossibility of string stability, from the LTI setting to any homogeneous controllers that can be nonlinear, time-varying, and locally communicating. We also prove that the impossibility holds for various variants on the most standard definition. Second, we prove that when perturbations are limited to the first subsystem of the chain, a PD controller reacting asymmetrically to one subsystem ahead and one behind can be tuned to achieve string stability. We give all results in a general discrete-time control setting which should be close to applications.