Some remarks on simultaneous stabilization problems of linear systems

In this paper, based on the results of complex analysis, we address and analyze some conclusions proposed by V.Blondel et al., which concern the simultaneous stabilization of three linear systems and a special bistabilization problem, named as “Chocolate Problem”. As for the simultaneous stabilization problem of three linear systems, it is shown that there is a slight flaw in the sufficiency part of Blondel´s proof. On the other hand, the claim is present, which illustrates that the theoretical upper bound of δ in Chocolate Problem given by Blondel et al. is not correct according to the work by Bergweiler et al.. Finally, the analysis to the new record proposed by Boston on the numerical bound is given, which shows the new bound is also not correct.