High-Order $A$ -Stable and $L$ -Stable State-Space Discrete Modeling of Continuous Systems

This paper presents a new method to map a state-space continuous-time model into an equivalent discrete state-space model. It is shown that the discrete model can approximate the continuous one to an arbitrary high-order which can be set by the user. In addition, it is demonstrated that the constructed discrete model is guaranteed stable, where it can be run in an A-stable or L-stable mode, depending on the application or user´s preference. The proposed mapping method is based on the single-step Obreshkov integration formulas that were proposed to solve ordinary differential equations. Preliminary performance experiments show superior accuracy compared to traditional discretization methods such as the Tustin method. Application of the proposed method to the discretization of analog filters demonstrates a significant accuracy in matching both of the magnitude and phase of the frequency response of the continuous system.