Stability robustness of LQ optimal regulators based on multirate sampling of plant output

The stability robustness of stable feedback loops, designed on the basis of multirate-output controllers (MROCs), is analyzed in this paper. For MROC-based feedback loops, designed in order to achieve LQ optimal regulation, we characterize additive and multiplicative norm-bounded perturbations of the loop transfer function matrix which do not destabilize the closed-loop system. New sufficient conditions for stability robustness, in terms of elementary MROC matrices, are presented. Moreover, guaranteed stability margins for MROC-based LQ optimal regulators are suggested for the first time. These margins are obtained on the basis of a fundamental spectral factorization equality, called the modified return difference equality, and are expressed directly in terms of elementary cost and system matrices. Sufficient conditions in order to guarantee the suggested stability margins are established. Finally, the connection between the suggested stability margins and the selection of cost weighting matrices is investigated and useful guidelines for choosing proper weighting matrices are presented.