[1991] Proceedings of the 30th IEEE Conference on Decision and Control
DOI: 10.1109/cdc.1991.261577
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A collection of robust control problems leading to LMIs

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Cited by 135 publications
(40 citation statements)
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“…Relations (30) and (31) are respectively equivalent to (7) and (8). The existence condition of a positive definite matrix P can result in the relation (9), which is the well-known completion lemma [25]. Furthermore, relation (10) implies that…”
Section: Resultsmentioning
confidence: 93%
“…Relations (30) and (31) are respectively equivalent to (7) and (8). The existence condition of a positive definite matrix P can result in the relation (9), which is the well-known completion lemma [25]. Furthermore, relation (10) implies that…”
Section: Resultsmentioning
confidence: 93%
“…One of the major differences between the proposed LFT approach and others are that the arbitrary perturbations, including LTV and nonlinear uncertainties, can also be treated by the LFT approach, where the Q-stability exactly captures this feature. In addition, the proposed LFT framework provides a systematic approach for gain-scheduled control design, where control solutions can be analytically constructed by solving the corresponding LMI' s independent of the parameters (see [28], [33], [27], and [31]), and therefore the conventional ad hoc point-wise controller design and curve-fitting procedures (see [39]) are avoided; moreover, the type of scheduling that results from this LFT approach guarantees the global stability and global performances even when the uncertainty varies arbitrarily fast and thus avoids any potential hazards arising from conventional scheduling [41], [39]. On the other hand, one disadvantage of the proposed approach, which emphasizes Q-stabilization, is that unless the uncertainties are arbitrary time-varying operators, the stability analysis on which the synthesis is based is potentially conservative [32].…”
Section: Introduction Inear Fractional Transformations (Lft's) Havmentioning
confidence: 99%
“…Some relevant results in particular the LMI characterizations, were also obtained in [33] in the parallel context of robust performance synthesis for linear fractional uncertain (discrete-time) systems. Though robust stability and robust performance can be uniformly treated as &-stability, the essential difference between the results in this paper and those in [33] lies in their approaches taken for synthesis problems; the approach using separation arguments for the stability synthesis problem in this paper cannot be naively extended to the performance synthesis problem because of the block-dependent nature of the designed controllers. Many extensions and generalizations have been done since the appearance of these two conference papers [34], [27], [31], [21].…”
Section: Introduction Inear Fractional Transformations (Lft's) Havmentioning
confidence: 99%
“…In particular, the development of Z?_ theory and structured singular value computation algorithms has greatly simplified the robust stability, performance analysis and controller design (see Doyle, 1982;Packard and Doyle, 1988;Doyle et al, 1989Doyle et al, , 1991Krause ef al., 1989;and references therein). For systems with time-varying uncertainties, some new results regarding the system robust stability have also been developed using the notion of quadratic stability (see Boyd andYang, 1989, Khargonekar et al, 1990;Doyle, 1990, Packard er al., 1991;Becker and Packard, 1991). However, the robust performance problem for systems with time-varying uncertainties has not been sufficiently explored.…”
Section: Introductionmentioning
confidence: 99%