A new upper bound for the real structured singular value

Gungah, S. K.; Malik, Usman; Jaimoukha, Imad M.; Halikias, George

doi:10.1109/cdc.2001.980106

Cited by 5 publications

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“…This was constructed by imposing the least-conservative bound on the projection of the structured uncertainty in the direction defined by the singular vectors corresponding to the smallest singular value of M . The method has been used successfully for real and mixed-type of structured uncertainty, resulting in algorithms with excellent computational performance [15,17]. In its dynamic version, this technique was also used in [14] to identify the set of all maximally-robust controllers which guarantee robust stability for the largest possible class of unstructured additive perturbations containing the uncertainty ball of maximum radius as a subset.…”

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confidence: 99%

On the Gap Between the Complex Structured Singular Value and Its Convex Upper Bound

Jaimoukha¹,

Halikias²,

Malik³

et al. 2006

SIAM J. Control Optim.

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Abstract. The gap between the complex structured singular value of a complex matrix M and its convex upper bound is considered. New necessary and sufficient conditions for the existence of the gap are derived. It is shown that determining whether there exists such a gap is as difficult as evaluating a structured singular value of a reduced rank matrix (whose rank is equal to the multiplicity of the largest singular value of M ). Furthermore, if an upper bound on this reduced rank problem can be obtained, it is shown that this provides an upper bound on the original problem that is lower than the convex relaxation upper bound. An example that illustrates our procedure is given. We also give the solution of several structured-approximation problems of independent interest.

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confidence: 99%