Stability and Stabilization of the Fractional-Order Power System With Time Delay

This brief investigates the problems of stability and stabilization of the fractional-order power system with time delay. The models of the fractional-order nonlinear and linearized delayed power system are established, respectively. Based on the theory of the fractional calculus and the Lyapunov functional technique, the relevant stability criteria are obtained. Meantime, new Lyapunov functionals are constructed, and the free-weighing matrix technique is introduced to reduce the conservatism of the criteria. The developed results can also be further extended to other similar nonlinear circuit systems. At last, effectiveness of the obtained results is demonstrated by simulation. Besides, simulation results indicate that the fractional-order model of the power system can more accurately describe the chaos phenomenon than the corresponding integer-order model, and the designed controller is valid.