Robust ∞ model reduction for the continuous fractional‐order two‐dimensional Roesser system: The 0 < ε ≤ 1 case

Abstract

This study analyzes the model reduction methods and the robust model reduction methods for the continuous fractional‐order (FO) two‐dimensional (2D) Roesser system with the FO ranging from 0 to 1. A sufficient LMI‐based condition is given by Projection Lemma, the FO‐stable‐region‐analyze method and matrix analysis, guaranteeing that the error system is stable and that its transfer function's ‐norm is bounded. Then, the approach to design the reduced‐model system of the original continuous FO 2D Roesser model is given. The robust model reduction methods for continuous FO 2D Roesser systems with polytopic uncertainties are proposed based on the results above. In the end, two numerical examples are used to demonstrate the effectiveness of the results.