System specific triangulations for the construction of CPA Lyapunov functions

<p style='text-indent:20px;'>Recently, a transformation of the vertices regular triangulation <inline-formula><tex-math id="M1">\begin{document}$ {\mathbb {R}}^n $\end{document}</tex-math></inline-formula> with in lattice id="M2">\begin{document}$ \mathbb{Z}^n was introduced, which distributes approximate rotational symmetry properties around origin. We prove that simplices transformed are id="M3">\begin{document}$ (h, d) $\end{document}</tex-math></inline-formula>-bounded, type non-degeneracy particularly useful numerical computation Lyapunov functions for nonlinear systems using CPA (continuous piecewise affine) method. Additionally, we discuss and give examples how this can be used together function linearization to compute system method considerably fewer than when triangulation.</p>