A novel general stability criterion of time-delay fractional-order nonlinear systems based on WILL Deduction Method

2020 ◽  
Vol 178 ◽  
pp. 328-344
Author(s):  
Zhe Zhang ◽  
Jing Zhang ◽  
Zhaoyang Ai ◽  
FanYong Cheng ◽  
Feng Liu
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Fractional Order ◽  
Stability Criterion ◽  
General Stability

Unknown input fractional-order functional observer design for one-side Lipschitz time-delay fractional-order systems

2019 ◽  
Vol 41 (15) ◽  
pp. 4311-4321 ◽  
Author(s):  
Mai Viet Thuan ◽  
Dinh Cong Huong ◽  
Nguyen Huu Sau ◽  
Quan Thai Ha
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Quadratic Function ◽  
Observer Design ◽  
Linear Matrix ◽  
Unknown Input ◽  
Functional Observer ◽  
The One

This paper addresses the problem of unknown input fractional-order functional state observer design for a class of fractional-order time-delay nonlinear systems. The nonlinearities consist of two parts where one part is assumed to satisfy both the one-sided Lipschitz condition and the quadratically inner-bounded condition and the other is not necessary to be Lipschitz and can be regarded as an unknown input, making the wider class of considered nonlinear systems. By taking the advantages of recent results on Caputo fractional derivative of a quadratic function, we derive new sufficient conditions with the form of linear matrix inequalities (LMIs) to guarantee the asymptotic stability of the systems. Four examples are also provided to show the effectiveness and applicability of the proposed method.

Robust asymptotic stability of interval fractional-order nonlinear systems with time-delay

2018 ◽  
Vol 355 (15) ◽  
pp. 7749-7763 ◽  
Author(s):  
Penghua Li ◽  
Liping Chen ◽  
Ranchao Wu ◽  
J.A. Tenreiro Machado ◽  
António M. Lopes ◽  
...  
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Fractional Order ◽  
Robust Asymptotic Stability

Bifurcation Analysis of Fractional Order Single Cell with Delay

2015 ◽  
Vol 25 (02) ◽  
pp. 1550020 ◽  
Author(s):  
Vedat Çelik
Keyword(s):  
Neural Networks ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Single Cell ◽  
Fractional Order ◽  
Bifurcation Analysis ◽  
Stability Criterion ◽  
Order Model ◽  
Bifurcation Points ◽  
Fractional Order Model

This paper presents the bifurcation analysis of fractional order model of delayed single cell which is proposed for delayed cellular neural networks with respect to the time delay τ. The bifurcation points, time delay τc, are determined by modified Mikhailov stability criterion for a range of fractional delayed cell order 0.3 ≤ q < 1. Numerical results obtained from Adams–Bashforth–Moulton method demonstrate that the supercritical Hopf bifurcation occurs in the system.

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