Stability conditions of linear discrete-time systems by characteristic equation coefficients

Abstract

A linear discrete-time system (LDTS) is deemed stable if the poles of its transfer function are located within the unit circle in the complex z-plane. To verify pole locations, techniques such as the Schur-Cohn criterion or the Jury test can be employed. Alternatively, an indirect approach involves mapping the interior of the unit circle to the left half-plane of the complex wplane using the bilinear transformation, which allows for the application of stability criteria designed for continuous-time systems. However, both direct and indirect methods become increasingly complex as the system's order increases, complicating the synthesis process. Given that modern automatic control systems, especially those involving dynamic objects, are often highdimensional, there is a significant need for simplified stability criteria to facilitate the synthesis process.