Delayed State-Feedback Fuzzy Control for Nonlinear Fractional Order Systems: An LMI Approach

This paper studies the problem of delayed state-feedback controller design for nonlinear fractional order systems. The effects of the time-varying delay on the controller design procedure are investigated. The proposed approach can not only be applicable for the systems that the controller intentionally created a time delay but also for the systems in which time delay inherently exists in the control input. Takagi-Sugeno (T-S) fuzzy model has been used for representing the nonlinear fractional order system. By adopting both state-feedback and delayed state- feedback approaches, new stabilization conditions are derived, which are indeed expressed in the framework of Linear Matrix Inequalities (LMIs). The stability proof is basically done based on a delay-dependent Lyapunov-Krasovskii Functional (LKF) and the usage of the slack matrices. Finally, the efficiency of the designed controller is validated by considering a gyroscope system as the running example.