Lebesgue Piecewise Affine Approximation of Nonlinear Systems and Its Application to Hybrid System Modeling of Biosystems

This paper proposes a new technique for approximating nonlinear systems by piecewise affine (PWA) system models. First, a method, called the Lebesgue piecewise affine approximation, is presented for approximately expressing nonlinear vector fields. Next, we derive an error bound of the PWA approximation systems in terms of the trajectories, and then show how to construct a PWA approximation system with an accuracy specified in advance. Finally, the proposed technique is applied to a gene regulatory network with nonlinear dynamics, and it is shown that the technique is useful for obtaining a PWA approximate system model for nonlinear systems