scholarly journals Problem and analysis of stability decidable theory for a class of fractional order nonlinear system

2013 ◽  
Vol 62 (2) ◽  
pp. 020502
Author(s):  
Li Li-Xiang ◽  
Peng Hai-Peng ◽  
Luo Qun ◽  
Yang Yi-Xian ◽  
Liu Zhe
Keyword(s):  
Nonlinear System ◽  
Fractional Order ◽  
Decidable Theory ◽  
Analysis Of Stability ◽  
Fractional Order Nonlinear System

Studying on the stability of fractional-order nonlinear system

2012 ◽  
Vol 70 (1) ◽  
pp. 475-479 ◽  
Author(s):  
Ling-Dong Zhao ◽  
Jian-Bing Hu ◽  
Jian-An Fang ◽  
Wen-Bing Zhang
Keyword(s):  
Nonlinear System ◽  
Fractional Order ◽  
The Stability ◽  
Fractional Order Nonlinear System

scholarly journals Random Response and Crossing Rate of Fractional Order Nonlinear System with Impact

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yang Zheng ◽  
Jiayin Wu ◽  
Ming Xu
Keyword(s):  
Nonlinear System ◽  
Fractional Order ◽  
Gaussian White Noise ◽  
Original System ◽  
Random Response ◽  
Unknown Parameters ◽  
Exact Probability ◽  
Mean Square Difference ◽  
The Impact ◽  
Fractional Order Nonlinear System

The random response and mean crossing rate of the fractional order nonlinear system with impact are investigated through the equivalent nonlinearization technique. The random additive excitation is Gaussian white noise, while the impact is described by a phenomenological model, which is developed from the actual impact process experiments. Based on the equivalent nonlinearization technique, one class of random nonlinear system with exact probability density function (PDF) solution of response is selected. The criterion of the appropriate equivalent nonlinear system is the similarity with the original system on the damping, stiffness, and inertia. The more similar, the higher the precision. The optimal unknown parameters of the equivalent random nonlinear system in the damping and stiffness terms are determined by the rule of smallest mean-square difference. In the view of equivalent nonlinearization technique, the response of the original system is the same as that of the equivalent system with the optimal unknown parameters in analytical solution manner. Then, the mean crossing rate is derived from stationary PDF. The consistence between the results from proposed technique and Monte Carlo simulation reveals the accuracy of the proposed analytical procedure.

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