An Extension of a Lyapunov‐Function‐Based Discretization Method for Asymptotically Stable Homogeneous Systems

ABSTRACT In this paper, we propose a family of discretization schemes that generalizes the Lyapunov‐function‐based scheme introduced in [49] for asymptotically stable homogeneous systems. We prove that if a convergent method with an order of consistency is used in the auxiliary stages of the Lyapunov‐function‐based method, then the whole discretization method is convergent and has an order of consistency . Additionally, we prove (under some mild conditions) that those discretization schemes produce discrete‐time systems that preserve both the properties of a Lyapunov function and the type of convergence (of the trajectories to the origin) associated with the discretized, continuous‐time system.