Stability and Performance Analysis of Single-Step FCS-MPC System Based on Regional ISS Theory

In recent years, finite-control-set model predictive control (FCS-MPC) has attracted significant attention in power electronic converter control, resulting in substantial research advancements. However, no formal method currently exists to prove the stability of FCS-MPC systems. Additionally, many application studies have yet to adequately address the relationship between the selection of design parameters and system performance. To address the lack of stability and performance guarantees in FCS-MPC system design, this paper investigates a class of single-step FCS-MPC systems. The analysis is based on regional input-to-state stability (ISS) theory. Sufficient conditions for ensuring regional stability are derived, and a method for estimating the system’s domain of attraction and ultimate bounded region is developed. Simulation experiments validated the analytical results and revealed the relationships between the domain of attraction and system stability, as well as between the ultimate bounded region and steady-state performance. The results indicate that appropriate parameter design can ensure system stability. Furthermore, the proposed method elucidates how changes in design parameters affect system stability and steady-state performance, providing a theoretical foundation for designing a class of FCS-MPC systems.