Stability robustness of LQ optimal regulators for the performance index with cross-product terms

Suggested are the guaranteed stability margins of LQ optimal regulators for the performance index with cross-product terms, using modified return difference equality. Sufficient conditions to guarantee the required stability margins are presented as well as the conditions to guarantee the stability margins of standard LQ optimal regulators. An example for LQ optimal control of a dc motor system is given to demonstrate how the weighting matrices can be chosen to guarantee the required stability margins.