Time-varying Lyapunov functions for nonautonomous nabla fractional order systems

2021 ◽  
Author(s):  
Yiheng Wei
Keyword(s):  
Fractional Order ◽  
Lyapunov Functions ◽  
Time Varying ◽  
Fractional Order Systems

Stability of Nonlinear Fractional-Order Time Varying Systems

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
Sunhua Huang ◽  
Runfan Zhang ◽  
Diyi Chen
Keyword(s):  
Laplace Transform ◽  
Fractional Order ◽  
Caputo Derivative ◽  
Local Stability ◽  
State Feedback ◽  
Sufficient Condition ◽  
Time Varying ◽  
Fractional Order Systems ◽  
Time Varying Systems ◽  
The Stability

This paper is concerned with the stability of nonlinear fractional-order time varying systems with Caputo derivative. By using Laplace transform, Mittag-Leffler function, and the Gronwall inequality, the sufficient condition that ensures local stability of fractional-order systems with fractional order α : 0<α≤1 and 1<α<2 is proposed, respectively. Moreover, the condition of the stability of fractional-order systems with a state-feedback controller is been put forward. Finally, a numerical example is presented to show the validity and feasibility of the proposed method.

Further Remarks on the Existence of Periodic Solutions of Linear Time Varying Periodic Fractional Order Systems

2017 ◽  
Author(s):  
XueFeng Zhang ◽  
YangQuan Chen
Keyword(s):  
Laplace Transform ◽  
Periodic Solutions ◽  
Fractional Order ◽  
Dynamic Systems ◽  
Linear Time ◽  
Periodic Systems ◽  
Time Varying ◽  
Fractional Order Systems ◽  
Order Linear ◽  
Existence Of Periodic Solutions

Existence of periodic solutions of fractional order dynamic systems is an important and difficult issue in fractional order systems field. In this paper, the non existence of completely periodic solutions and existence of partly periodic solutions of fractional order linear time varying periodic systems and fractional order nonlinear time varying periodic systems are discussed. A new property of Laplace transform of periodic function is derived. The non existences of completely periodic solutions of fractional order linear time varying periodic systems and fractional order nonlinear time varying periodic fractional order systems are presented by Laplace transform method and contradiction approach. The existence of partly periodic solutions of fractional order dynamic systems are proved by constructing numerical examples and considering Laplace transform property approaches. The examples and state figures are given to illustrate the effectiveness of conclusion presented.

Convex Lyapunov functions for stability analysis of fractional order systems

2017 ◽  
Vol 11 (7) ◽  
pp. 1070-1074 ◽  
Author(s):  
Weisheng Chen ◽  
Hao Dai ◽  
Yanfei Song ◽  
Zhengqiang Zhang
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Lyapunov Functions ◽  
Fractional Order Systems

Lyapunov functions for fractional order systems

2014 ◽  
Vol 19 (9) ◽  
pp. 2951-2957 ◽  
Author(s):  
Norelys Aguila-Camacho ◽  
Manuel A. Duarte-Mermoud ◽  
Javier A. Gallegos
Keyword(s):  
Fractional Order ◽  
Lyapunov Functions ◽  
Fractional Order Systems
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