2007
DOI: 10.1016/j.arcontrol.2007.09.002
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Nonsmooth optimization and robust control

Abstract: Many questions of robust control analysis and synthesis fundamentally involve nonsmooth sets and functions, and their variational properties. Central examples include distances to instability and uncontrollability, the H 1 norm, and pseudospectra. This plenary presentation at the Fifth IFAC Symposium on Robust Control Design (2006), surveys what current ideas from nonsmooth analysis say about the structure and conditioning of such functions and sets, and their numerical optimization. The presentation focuses o… Show more

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Cited by 16 publications
(7 citation statements)
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“…for all ¹t j > 0º 1 j D1 and for i D 1, 2, : : : , p. To construct a state feedback controller for the uncertain system (15), (3), (17), we apply an S -procedure type result [9, Theorem 4.1] (see Appendix A.1) by introducing scaling constants 1 > 0, : : : , kCp > 0 corresponding to the IQCs (3), (17). Thus, the state equations (15) can be represented as follows: ,…”
Section: An Equivalent Robust H 1 Control Problemmentioning
confidence: 99%
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“…for all ¹t j > 0º 1 j D1 and for i D 1, 2, : : : , p. To construct a state feedback controller for the uncertain system (15), (3), (17), we apply an S -procedure type result [9, Theorem 4.1] (see Appendix A.1) by introducing scaling constants 1 > 0, : : : , kCp > 0 corresponding to the IQCs (3), (17). Thus, the state equations (15) can be represented as follows: ,…”
Section: An Equivalent Robust H 1 Control Problemmentioning
confidence: 99%
“…Theorem 1 Supposeˇ1 > 0, : : : ,ˇp > 0 are given constants such that the uncertain system (15), (3), (17) is absolutely stabilizable with a prescribed disturbance attenuation level > 0 via a controller of form (6),…”
Section: Assumptionmentioning
confidence: 99%
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