In this paper, we aim to solve the stabilization problem for a large class of fractional-order nonautonomous systems via linear state feedback control and adaptive control. By constructing quadratic Lyapunov functions and utilizing a new property for Caputo fractional derivative we derive some sufficient conditions for the global asymptotical stabilization of a class of fractional-order nonautonomous systems. We give two illustrative examples to validate the effectiveness of the theoretical results.

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The analysis of the switch status of each unit module of a cascaded multi-level inverter reveals that the working condition of the switch of a chopper arm causes unnecessary switching under the conventional unipolar sinusoidal pulse width modulation (SPWM).With an increase in the number of cascaded multilevel inverters, the superposition of unnecessary switching gradually occurs. In this work, we propose an improved SPWM strategy to reduce switching in cascaded multilevel inverters. Specifically, we analyze the switch state of the switch tube of a chopper arm of an H-bridge unit. The redundant switch is then removed, thereby reducing the switching frequency. Unlike the conventional unipolar SPWM technique, the improved SPWM method greatly reduces switching without altering the output quality of inverters. The conventional unipolar SPWM technique and the proposed method are applied to a five-level inverter. Simulation results show the superiority of the proposed strategy. Finally, a prototype is built in the laboratory. Experimental results verify the correctness of the proposed modulation strategy.

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