Analyzing the Transient Process and the Realizability of Fractional Systems via Intermittent Control

In this paper, we have studied the transient process and the realizability of fractional systems via intermittent control. For any system under intermittent control input, a transient oscillation process is inevitable when the input switches, which is irrelevant to mathematical model. But this process is usually neglected when considering the achievements of fractional intermittent control systems as the initial value is changed by the switching input. The obtained theoretical results cannot agree with the real physical model. The input signal is treated as a piecewise signal by means of convolution operation and unit step function, and the output is drawn by convoluting the control input with a time decay function. We have drawn the conclusions that the initial value of the fractional model can not be updated by any outer input and that a transient process must exist that is related to all historic process and the memory property of a fractional system. If the response function of a system is taken as the time decay function, the results obtained are in good agreement with the actual model and can be used to analyze the transient phenomena in nature. Some examples are presented to verify our theoretical achievements.