Describing Functions for Scalar Information Channels Subject to Quantization and Packet Loss

Abstract

Many of today's robot applications depend on wireless communications, whose performance can impact the whole system. To support analysis of feedback control through limited channels, we develop describing functions (DFs) for three variations on the series interconnection of a quantizer, a binary erasure channel, and decoder for a single input single output (SISO) system. The key steps in our derivation hold when the decoder is a linear-quadratic-Gaussian (LQG)-type control, a zero-output decoder, or a hold-output decoder. We confirm the accuracy of the new formulas and provide an example showing limit cycle behavior.