Non-fragile Finite-Time Guaranteed Cost Control for a Class of Singular Caputo Fractional-Order Systems with Uncertainties

In the present paper, for the first time, we consider the problem of non-fragile finite-time guaranteed cost control for a class of fractional-order singular systems with norm-bounded uncertainties. Firstly, we establish a linear quadratic cost function based on the integral of integer order, which serves practical purposes and acts as a performance measure index for the closed-loop system. Then, leveraging finite-time boundedness theory, inequality techniques, and fractional-order calculus properties, we propose a non-fragile state feedback controller that ensures regularity, impulse-free, and finite-time boundedness in the closed-loop system. Furthermore, we establish an upper limit for the performance index. The resulting findings are reliant on the order of the considered fractional-order systems and are obtained through the use of strict linear matrix inequalities (LMIs), devoid of any equality restrictions. Finally, two simulation examples are provided to validate the effectiveness of the proposed method.