Work by John C. Doyle, IEEE TAC 1978

Keywords: Robust control, optimal control, robustness margins, linear quadratic Gaussian, linear quadratic regulator, Kalman filter

Summary

In this classic paper with the famously short 3-word long abstract “there are none”, it is shown by counterexample that linear-quadratic Gaussian (LQG) regulators do not possess any gain or phase stability robustness margins. This stands in stark contrast to the case of linear quadratic regulators (LQR) which were shown a year prior by Safanov and Athens to possess impressive guaranteed 6dB gain and 60 degree phase margins.

Read the paper here or from IEEE Xplore.

See Stephen Tu’s nice walkthrough of this paper.