New Criteria for Guaranteed Cost Control of Nonlinear Fractional-Order Delay Systems: a Razumikhin Approach

The Krasovskii-Lyapunov second method provides a powerful approach to stability analysis of nonlinear systems; however, it is not always effectively applied for fractional-order systems (FOSs) with delay. In this paper, we investigate the problem of guaranteed cost control of fractional-order delay systems subject to nonlinear perturbations and parametric time-varying uncertainties. By using fractional Razumikhin theorem, new sufficient conditions are derived for designing a guaranteed cost controller, which not only makes the closed-loop system asymptotically stable but also guarantees an adequate cost level of performance. Compared with the existing results on the integer-order control systems, our results are more effective and convenient for testing and application. The proposed approach allows us to derive stability criteria of linear uncertain FOSs with delay. Finally, numerical examples are given to show the effectiveness of the obtained results.