Robust H∞ Model Reduction for Fractional-order Two-dimensional Continuous Roesser System: The 1 < ε < 2 Case

This study explores robust H
∞
model reduction techniques for the two-dimensional (2D) fractional-order (FO) continuous Roesser system, where the FO is within the interval (1, 2). The FO-stable-region-analyze and matrix analysis methods are used to provide a sufficient condition to solve the H
∞
model reduction issue for the 2D FO Roesser system in the form of linear matrix inequalities (LMIs). This condition ensures the stability of the error system and bounds the H
∞
-norm of its transfer function. The manuscript proceeds by giving a procedure for designing a reduced-order system model of the FO 2D continuous Roesser system. Robust H
∞
model reduction methods for FO 2D continuous Roesser systems with parameter uncertainties are then proposed based on the aforementioned results. To demonstrate the effectiveness of the proposed methods, a numerical example is provided.