Toward a Comprehensive Impossibility Result for String Stability - Farnam, Arash; Sarlette, Alain (IEEE transactions on automatic control, 2020)
We provide a comprehensive impossibility result toward 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 the existing results, from the linear time-invariant (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 L_2 -type standard and a bounded-input implies bounded-output (BIBO) type criterion. All the results hold for a general discrete-time controller, which should cover most applications.