© 1998 by Institute of Mathematics and its Applications
Stability robustness to unstructured uncertainties of linear systems controlled on the basis of the multirate sampling of the plant output
Division of Computer Science, Department of Electrical and Computer Engineering, National Technical University of Athens Zographou, 15773, Athens, Greece
Section of Mathematical Analysis, Department of Mathematics, University of Athens Panepistemiopolis, 15784, Athens, Greece
The stability robustness of stable feedback loops designed on the basis of multirate-output controllers (MROCs) is analysed in this paper. For MROC-based feedback loops, designed to achieve stabilization through pole placement or deterministic linear-quadratic (LQ) optimal regulation, we characterize additive or multiplicative norm-bounded perturbations of the loop transfer-function matrix that do not destabilize the closed-loop system. New sufficient stability conditions in terms of the elementary MROC matrices are presented, for both static and (stable) dynamic MROCs. Moreover, lower bounds for the minimum singular values of the return-difference and of the inverse return-difference matrices are suggested for all cases of the aforementioned MROC-based stable feedback designs. Also suggested are guaranteed stability margins for MROC-based pole placers and LQ optimal regulators. A comparison between the suggested stability margins for static and (stable) dynamic MROCs is presented, while the superiority of these margins over known stability margins for deterministic LQ optimal regulators is identified. Finally, an analysis of the deficiency of the aforementioned stablity margins is presented for cases where the MROC feedback gains become very large, and useful guidelines are suggested for the choice of the sampling period and of the output multiplicities of the sampling to avoid this deficiency.
E-mail: karvan{at}control.ece.ntua.gr