Title :
The largest singular value of eXA0e -X is convex on convex sets of commuting matrices
Author :
Sezginer, Renan Sezer ; Overton, Michael L.
Author_Institution :
Courant Inst. of Math. Sci., New York Univ., NY, USA
fDate :
2/1/1990 12:00:00 AM
Abstract :
A short and direct proof of the convexity property is given. It is shown that the theorem applies to any convex, commuting set of matrices in RnXn, where A0∈RnXn is fixed. It is also shown that the result does not hold if X is permitted to be a general square matrix. A counterexample is supplied for noncommuting matrices
Keywords :
matrix algebra; optimisation; commuting matrices; convex sets; convexity property; general square matrix; largest singular value; matrix algebra; noncommuting matrices; optimisation; Adaptive control; Asymptotic stability; Automatic control; Differential equations; Feedback amplifiers; Gaussian processes; Network synthesis; Programmable control; Robust control; Uncertainty;
Journal_Title :
Automatic Control, IEEE Transactions on
