Abstract
In this study, we focus on the controllability of fractional-order damped systems in linear and nonlinear cases with multiple time-varying delays in control. For the linear system based on the Mittag-Leffler matrix function, we define a controllability Gramian matrix, which is useful in judging whether the system is controllable or not. Furthermore, in two special cases, we present serval equivalent controllable conditions which are easy to verify. For the nonlinear system, under the controllability of its corresponding linear system, we obtain a sufficient condition on the nonlinear term to ensure that the system is controllable. Finally, two examples are given to illustrate the theory.
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Hua-cheng ZHOU and Chun-hai KOU designed the research. Bin-bin HE and Hua-cheng ZHOU drafted the manuscript. Chun-hai KOU helped organize the manuscript. Bin-bin HE and Hua-cheng ZHOU revised and finalized the paper.
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Bin-bin HE, Hua-cheng ZHOU, and Chun-hai KOU declare that they have no conflict of interest.
Project supported by the National Natural Science Foundation of China (No. 61803386) and the Natural Science Foundation of Shanghai, China (No. 19ZR1400500)
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He, Bb., Zhou, Hc. & Kou, Ch. Controllability of fractional-order damped systems with time-varying delays in control. Front Inform Technol Electron Eng 21, 844–855 (2020). https://doi.org/10.1631/FITEE.1900736
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DOI: https://doi.org/10.1631/FITEE.1900736