A revisit of the stability robustness of linear quadratic regulators

In quadratic optimal control theory, the multivariable linear quadratic regulator is guaranteed to have excellent stability margins if the weight on the control inputs is diagonal. However, for the non-diagonal case, it may suffer from poor robustness. In this paper, these robustness properties are studied in relation to weight selection. Specifically, in the non-diagonal case, guaranteed stability margins are presented. This gives a formal mathematical basis for guidelines for the designer to improve stability robustness. The results are demonstrated by numerical examples.