Numerical construction of LISS Lyapunov functions under a small gain condition

We provide a homotopy algorithm that computes a decay point of a monotone operator, i.e., a point whose image under the monotone operator is strictly smaller than the preimage. For this purpose we use a fixed point algorithm and provide a function whose fixed points correspond to decay points of the monotone operator. This decay point plays a crucial role in checking, in a semi-global fashion, the local input-to-state stability of an interconnected system numerically and in the numerical construction of local input-to-state stability (LISS) Lyapunov functions. We give some improvements of this algorithm and show the advantage to an earlier approach based on the algorithm of Eaves.