Can one introduce an equality constraint into the GEVP problem?

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I am currently tackling a Generalized EigenValue minimization under LMI constraints with LMI toolbox(https://www.mathworks.com/help/releases/R2019b/robust/ref/gevp.html).
Also I want to add an equality constraint to the decisive variable, something like AX=0.
Dose anyone know anything about it? Please help!

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