LMI-Based Stability Conditions for Continuous Fractional-Order Two-Dimensional Fornasini-Marchesini First Model

In this brief, the structural stability of continuous fractional-order (FO) two-dimensional (2D) Fornasini-Marchesini (FM) first model is investigated. Firstly, the bivariate polynomial-based stability condition is equivalently transformed to be in more tractable form. Then, based on generalized KYP lemma, the transformed conditions are further reduced into the feasibility problem of linear matrix inequalities (LMIs). The main contribution is to establish the LMI-based stability conditions for continuous FO 2D FM first model. The results can be applied in the cases with FO
$\alpha _{i} \in (0,2)$
and be no conservative when the FO in the second dimension
$\alpha _{2} \in [1,2$
). Lastly, the example is provided to verify the efficiency.