scholarly journals Finite-Time Stability of Fractional-Order Time-Varying Delays Gene Regulatory Networks with Structured Uncertainties and Controllers

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Zhaohua Wu ◽  
Zhiming Wang ◽  
Tiejun Zhou
Keyword(s):  
Fractional Order ◽  
Gene Regulatory Networks ◽  
Finite Time ◽  
Regulatory Networks ◽  
State Feedback ◽  
Time Varying ◽  
Time Stability ◽  
Feedback Controllers ◽  
Finite Time Stability ◽  
Gene Regulatory

In this paper, we investigate a class of fractional-order time-varying delays gene regulatory networks with structured uncertainties and controllers (DFGRNs). Our contributions lie in three aspects: first, a necessary and sufficient condition on the existence of the solution for the DFGRNs is given by using the properties of the Riemann–Liouville fractional derivative and Caputo’s fractional derivative; second, the unique solution of the DFGRNs is proved under given initial function and certain condition; third, some novel sufficient conditions on finite-time stability of the DFGRNs are established by using a generalized Gronwall inequality and norm technique, and some conclusions on the finite-time stability of the DFGRNs with memory state-feedback controllers are reached, and those conditions and conclusions depend on the fractional order of the DFGRNs. One of the most interesting findings is that the “estimated time” of the finite-time stability is indeed related to the structured uncertainties, state-feedback controllers, time delays, and the fractional order of the system.

scholarly journals Finite-Time Boundedness Control of Time-Varying Descriptor Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Xiaoming Su ◽  
Yali Zhi ◽  
Qingling Zhang
Keyword(s):  
Control Problem ◽  
Finite Time ◽  
State Feedback ◽  
Descriptor Systems ◽  
Necessary Condition ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Finite Time Boundedness ◽  
Sufficient And Necessary Condition

This paper mainly studies a control problem of finite-time boundedness of time-varying descriptor systems. Firstly, a sufficient and necessary condition of finite-time stability is given, then a sufficient condition of finite-time boundedness for time-varying descriptor systems is given. Secondly, we analyze the finite-time boundedness control problem and design the finite-time state feedback controller; the controller is given based on LMIs for time-varying descriptor systems and time-varying uncertain descriptor systems, respectively. Finally, a numerical example is given to prove the effectiveness of the method.

scholarly journals NEW RESULTS ON FINITE-TIME STABILITY FOR NONLINEAR FRACTIONAL ORDER LARGE SCALE SYSTEMS WITH TIME VARYING DELAY AND INTERCONNECTIONS

2020 ◽  
Vol 225 (02) ◽  
pp. 52-57
Author(s):  
Phạm Ngọc Anh ◽  
Nguyễn Trường Thanh ◽  
Hoàng Ngọc Tùng
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Large Scale ◽  
Time Varying ◽  
Time Stability ◽  
Large Scale Systems ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Varying Delay

Bài báo này khảo sát tính ổn định hữu hạn của một lớp hệ quy mô lớn cấp phân số có trễ biến thiên và nhiễu phi tuyến. Sử dụng bất đẳng thức Gronwall tổng quát, một điều kiện đủ cho ổn định hữu hạn của các hệ này được thiết lập thông qua hàm Mittag-Leffler. Kết quả thu được sau đó được áp dụng cho hệ bất định và hệ không ôtonom có trễ biến thiên và nhiễu phi tuyến.

scholarly journals Global uniform asymptotical stability for fractional-order gene regulatory networks with time-varying delays and structured uncertainties

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zhaohua Wu ◽  
Zhiming Wang ◽  
Tiejun Zhou
Keyword(s):  
Fractional Order ◽  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Time Varying ◽  
The Novel ◽  
Razumikhin Technique ◽  
Gene Regulatory ◽  
The Stability

AbstractIn this paper, we investigate a class of fractional-order gene regulatory networks with time-varying delays and structured uncertainties (UDFGRNs). First, we deduce the existence and uniqueness of the equilibrium for the UDFGRNs by using the contraction mapping principle. Next, we derive a novel global uniform asymptotic stability criterion of the UDFGRNs by using a Lyapunov function and the Razumikhin technique, and the conditions relating to the criterion depend on the fractional order of the UDFGRNs. Finally, we provide two numerical simulation examples to demonstrate the correctness and usefulness of the novel stability conditions. One of the most interesting findings is that the structured uncertainties indeed have an impact on the stability of the system.

scholarly journals Lyapunov Approach for Almost Periodicity in Impulsive Gene Regulatory Networks of Fractional Order with Time-Varying Delays

2021 ◽  
Vol 5 (4) ◽  
pp. 268
Author(s):  
Ivanka Stamova ◽  
Gani Stamov
Keyword(s):  
Fractional Order ◽  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
Sufficient Conditions ◽  
Almost Periodicity ◽  
Time Varying ◽  
Almost Periodic ◽  
Proposed Model ◽  
Periodic State ◽  
Gene Regulatory

This paper investigates a class of fractional-order delayed impulsive gene regulatory networks (GRNs). The proposed model is an extension of some existing integer-order GRNs using fractional derivatives of Caputo type. The existence and uniqueness of an almost periodic state of the model are investigated and new criteria are established by the Lyapunov functions approach. The effects of time-varying delays and impulsive perturbations at fixed times on the almost periodicity are considered. In addition, sufficient conditions for the global Mittag–Leffler stability of the almost periodic solutions are proposed. To justify our findings a numerical example is also presented.

Sign in / Sign up

Export Citation Format

Share Document