TY - JOUR
T1 - Structured singular value of a repeated complex full-block uncertainty
AU - Mushtaq, Talha
AU - Bhattacharjee, Diganta
AU - Seiler Jr, Peter J
AU - Hemati, Maziar S.
N1 - Publisher Copyright:
© 2024 John Wiley & Sons Ltd.
PY - 2024
Y1 - 2024
N2 - The structured singular value (SSV), or (Formula presented.), is used to assess the robust stability and performance of an uncertain linear time-invariant system. Existing algorithms compute upper and lower bounds on the SSV for structured uncertainties that contain repeated (real or complex) scalars and/or nonrepeated complex full-blocks. This paper presents algorithms to compute bounds on the SSV for the case of repeated complex full-blocks. This specific class of uncertainty is relevant for the input-output analysis of many convective systems, such as fluid flows. Specifically, we present a power iteration to compute the SSV lower bound for the case of repeated complex full-blocks. This generalizes existing power iterations for repeated complex scalars and nonrepeated complex full-blocks. The upper bound can be formulated as a semi-definite program (SDP), which we solve using a standard interior-point method to compute optimal scaling matrices associated with the repeated full-blocks. Our implementation of the method only requires gradient information, which improves the computational efficiency of the method. Finally, we test our proposed algorithms on an example model of incompressible fluid flow. The proposed methods provide less conservative bounds as compared to prior results, which ignore the repeated full-block structure.
AB - The structured singular value (SSV), or (Formula presented.), is used to assess the robust stability and performance of an uncertain linear time-invariant system. Existing algorithms compute upper and lower bounds on the SSV for structured uncertainties that contain repeated (real or complex) scalars and/or nonrepeated complex full-blocks. This paper presents algorithms to compute bounds on the SSV for the case of repeated complex full-blocks. This specific class of uncertainty is relevant for the input-output analysis of many convective systems, such as fluid flows. Specifically, we present a power iteration to compute the SSV lower bound for the case of repeated complex full-blocks. This generalizes existing power iterations for repeated complex scalars and nonrepeated complex full-blocks. The upper bound can be formulated as a semi-definite program (SDP), which we solve using a standard interior-point method to compute optimal scaling matrices associated with the repeated full-blocks. Our implementation of the method only requires gradient information, which improves the computational efficiency of the method. Finally, we test our proposed algorithms on an example model of incompressible fluid flow. The proposed methods provide less conservative bounds as compared to prior results, which ignore the repeated full-block structure.
KW - method of centers
KW - repeated complex full-blocks
KW - structured singular value
KW - structured uncertainty
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U2 - 10.1002/rnc.7238
DO - 10.1002/rnc.7238
M3 - Article
AN - SCOPUS:85185463402
SN - 1049-8923
JO - International Journal of Robust and Nonlinear Control
JF - International Journal of Robust and Nonlinear Control
ER -