In this paper stability analysis of fractionalorder nonlinear systems is studied. An extension of Lyapunov direct method for fractional-order systems using Bihari's and Bellman-Gronwall's inequality and a proof of comparison theorem for fractional-order systems are proposed.
In this paper a novel controller for a flexible link manipulator based on fractional calculus is proposed. A hybrid system that combines the advantages in terms of robustness of the fractional control and the sliding mode control is proposed. Due to adding the extra degree of freedom, the fractional order sliding mode controller can achieve better control performance than the integer order sliding mode controller. For the problem of determining the design parameters, the particle swarm optimization (PSO) algorithm is used. The proposed controller is applied for a single‐link flexible manipulator robot. Finally, the performance and the significance of the closed loop system are investigated. The simulation results signify the performance of the proposed controller.
Robust control of fractional-order Liu system is addressed in this paper. The proposed approach relies on sliding mode control being established on a novel fractional-order integral type sliding surface. Theoretically, based on classical Lyapunov stability theorem, it has been shown that under suitable conditions, the proposed controller guarantees the system's stability. Further, it is shown that the method presented is capable for both commensurate and incommensurate systems. In order to reduce the chattering effect, a fuzzy logic controller is employed. Numerical simulations verify these results.
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