  Finsler's lemma is a classic mathematical result with applications in control
and optimization. When the lemma is applied to parameter-dependent LMIs, as
such those that arise from problems of robust stability, the extra variables
introduced by this lemma also become dependent on this parameter. This
technical note presents some sufficient conditions which ensure, without losing
generality, that these extra variables can assume a simple functional
dependence on the parameters as continuity or even independence. The results
allow avoiding an unnecessary use of a more functionally complicated
parameter-dependent variable that increases the search computational burden
without reducing the conservatism of the solution.
