Frequency-domain approach to the absolute stability analysis of discrete-time linear-quadratic regulators

A frequency-domain approach to the absolute stability analysis of multivariable time-invariant discrete-time linear quadratic regulators is developed in the paper. An imbedding form of a fundamental equality relating the return-difference and the open-loop transfer matrices is the key for the application of the Popov criterion in the analysis. This imbedding form also establishes a necessary condition for a closed-loop matrix transfer function to have been obtained through an LQ design.