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

Abstract

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 , 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.