Abstract
By \(\mathcal{A}\subset \mathcal{B}\) we mean that all elements of \(\mathcal{A}\) are elements of ℬ, that is, inclusion is non-proper unless \(\mathcal{A}\neq \mathcal{B}\) is specified. Set union and intersection are denoted ∪, ∩. A set \(\mathcal{A}\) of points in ℝ n is convex if it contains all segments with endpoints in \(\mathcal{A}\). A set \(\mathcal{A}\) is symmetric if it contains − a whenever it contains a. A symmetric convex set contains the origin.
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The interesting aspect of the Schur complement lies in transforming nonlinear matrix inequalities of order n (like the LMI on the lhs in the variables S and T) into linear matrix inequalities of order 2n (like the one on the rhs in the same variables).
References
Golub GH, Van Loan CF (1983) Matrix computations. John Hopkins University Press, Baltimore
Kurzhanski AB, Vallyi I (1996) Ellipsoidal calculus for estimation and control. Birkhauser, Boston
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© 2013 Springer Science+Business Media New York
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Caravani, P. (2013). Appendix. In: Modern Linear Control Design. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6943-8_9
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DOI: https://doi.org/10.1007/978-1-4614-6943-8_9
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