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Why were these constants picked in this Lyapunov function and how did the author arrive at the final Lyapunov function?

Consider the following paper:

https://reader.elsevier.com/reader/sd/pii/S0893965917301611?token=4D46CE0CD4DEC9D9B6A988B5C5EBD28E17BA830CC4004D7262A209F791CC7AC11BA4C3183E572636E3A9E8113FBB17EB&originRegion=eu-west-1&originCreation=20220214125151

The methodology is understood in this paper apart from some technical things; How did the author arrive at constants $m_i, i=1,...,5$? They achieved this by killing the variable terms($xu, xv, z, u, v, yu, yv$), however when I try solving the system, it outputs all $m_i$'s equalling zero. Can someone show a detailed answer how they arrived at these constants and how they got their final form of the Lyapunov function(page 168)?

Math
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