Allowable parameter variations and robustness recovery in LQG regulators

In this paper, the bounds of allowable parameter variations in the LQG regulator for fixed weighting matrices are obtained and the asymptotic properties of these bounds with respect to weighting matrices are analysed. It is shown that the guaranteed bounds of allowable parameter variations, which are independent of weighting matrices, are often small but not necessarily small under some conditions. It is also shown that under some conditions, the allowable bounds of the LQG regulator can become as large as those of the LQ regulator. In addition, a loop transfer recovery method for perturbed systems is derived under which the LQG regulator may possess the same robustness as the LQ regulator. Examples are given to validate these results.