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Several algorithms have been suggested to parameterize continuous and piecewise affine Lyapunov functions for nonlinear systems in various settings. In these algorithms linear constraints are formulated for the values of a Lyapunov function at all vertices of a simplicial complex. They are then either solved using convex optimization or computed by other means and then verified. Originally these algorithms were designed for continuous-time systems and their adaptation to discrete-time systems and control systems poses some challenges in designing and implementing efficient algorithms and data structures for simplicial complexes. In this paper we discuss several of these and give efficient implementations in C++.

Efficient Algorithms for Simplicial Complexes Used in the Computation of Lyapunov Functions for Nonlinear Systems