期刊
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
卷 20, 期 3, 页码 905-913出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2014.05.013
关键词
Lyapunov stability theory; Fractional; Delay; Integral derivative
类别
资金
- National Natural Science Foundation of China [61304062, 61174066, 61371111, 61371112]
The difficulty of fractional direct Lyapunov stable theorem lies in that how to design a positive definite function V and easily ascertain whether fractional derivative of the function V is less than zero. In view of this difficulty, we propose a Lyapunov stability theorem for fractional system without delay and extend the newly proposed theorem to fractional system with delay. The obvious difference of the proposed theory with the fractional Lyapunov direct theory is taking the integer derivative instead of the fractional derivative of the positive definite function V. Four examples are provided to illustrate the proposed theorem. The studying results in this paper show that the proposed theorem is not only applicable to the fractional autonomous system with and without delay, but also applicable to the fractional non-autonomous system with and without delay. (C) 2014 Elsevier B.V. All rights reserved.
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