Finite Frequency H∞ Control of Fractional-Order Continuous–Discrete 2-D Roesser Models

The
$H_{\infty }$
control problem of fractional-order continuous-discrete 2D Roesser models in the finite frequency is investigated in this brief. Firstly, based on the frequency-partitioning method and generalized Kalman–Yakubovi
$\check {\text {c}}$
–Popov lemma, the finite frequency bounded real lemmas in form of linear matrix inequalities (LMIs) are proposed, which can be solved by LMI solvers immediately. Then, the
$H_{\infty }$
state feedback controller is designed, and the existence conditions are established in form of bilinear matrix inequalities (BMIs). Moreover, by the provided iterative algorithm, these BMI-based conditions can be solved based on LMIs. Finally, the numerical examples are provided verify the validity of our results.