Robust stability and stabilization of continuous-discrete fractional-order 2D Fornasini-Marchesini second model with interval uncertainties

This paper investigates the robust stability and stabilization problems of continuous-discrete fractional-order two-dimensional Fornasini-Marchesini second model with interval uncertainties. Firstly, for the nominal model with fractional-order alpha is an element of(0,2)$$ \alpha \in \left(0,2\right) $$, the unified LMI-based stability conditions are presented by general description of stable root-clustering sets. Secondly, these stability conditions are transformed to be more tractable for stabilization, and the LMI/BMI-based stabilization conditions are established via state feedback controllers. Meanwhile, one algorithm is proposed to solve the BMI-based conditions. Thirdly, facing interval uncertainties in this model, the LMI-based robust stability conditions and LMI/BMI-based robust stabilization conditions are established. Lastly, two examples are given to show the validity of our robust stability and stabilization results.