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On cone-invariant linear matrix inequalities

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2 Author(s)
Parrilo, P.A. ; Dept. of Control & Dynamical Syst., California Inst. of Technol., Pasadena, CA ; Khatri, S.

An exact solution for a special class of cone-preserving linear matrix inequalities (LMIs) is developed. By using a generalized version of the classical Perron-Frobenius theorem, the optimal value is shown to be equal to the spectral radius of an associated linear operator. This allows for a much more efficient computation of the optimal solution using, for instance, power iteration-type algorithms. This particular LMI class appears in the computation of upper bounds for some generalizations of the structured singular value μ (spherical μ) and in a class of rank minimization problems previously studied. Examples and comparisons with existing techniques are provided

Published in:

Automatic Control, IEEE Transactions on  (Volume:45 ,  Issue: 8 )

Date of Publication:

Aug 2000

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