Journal Article

Stability robustness to unstructured uncertainties of linear systems controlled on the basis of the multirate sampling of the plant output

K. G. ARVANITIS and G. KALOGEROPOULOS

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 15, issue 3, pages 241-268
Published in print September 1998 | ISSN: 0265-0754
Published online September 1998 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/15.3.241
Stability robustness to unstructured uncertainties of linear systems controlled on the basis of the multirate sampling of the plant output

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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.

Journal Article.  0 words. 

Subjects: Mathematics

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