Design of H ∞/Passive State Feedback Control for Delayed Fractional Order Gene Regulatory Networks Via New Improved Integral Inequalities

2021 ◽  
Author(s):  
Padmaja N. ◽  
Balasubramaniam P.
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
State Feedback ◽  
State Feedback Control ◽  
Integral Inequalities ◽  
Passive State ◽  
Gene Regulatory

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.

Global stability analysis of fractional-order gene regulatory networks with time delay

2019 ◽  
Vol 12 (06) ◽  
pp. 1950067 ◽  
Author(s):  
Zhaohua Wu ◽  
Zhiming Wang ◽  
Tiejun Zhou
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Gene Regulatory Networks ◽  
Existence And Uniqueness ◽  
Regulatory Networks ◽  
Lyapunov Method ◽  
Regulation Mechanism ◽  
Global Stability Analysis ◽  
Gene Regulatory ◽  
The Stability

Fractional-order gene regulatory networks with time delay (DFGRNs) have proven that they are more suitable to model gene regulation mechanism than integer-order. In this paper, a novel DFGRN is proposed. The existence and uniqueness of the equilibrium point for the DFGRN are proved under certain conditions. On this basis, the conditions on the global asymptotic stability are established by using the Lyapunov method and comparison theorem for the DFGRN, and the stability conditions are dependent on the fractional-order [Formula: see text]. Finally, numerical simulations show that the obtained results are reasonable.

scholarly journals H∞ state feedback control of commensurate fractional order systems

2013 ◽  
Vol 46 (1) ◽  
pp. 54-59 ◽  
Author(s):  
Lamine Fadiga ◽  
Jocelyn Sabatier ◽  
Christophe Farges
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
State Feedback ◽  
State Feedback Control ◽  
Fractional Order Systems

scholarly journals New Results on Synchronization of Fractional-Order Memristor‐Based Neural Networks via State Feedback Control

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Xiaofan Li ◽  
Yuan Ge ◽  
Hongjian Liu ◽  
Huiyuan Li ◽  
Jian-an Fang
Keyword(s):  
Neural Networks ◽  
Feedback Control ◽  
Fractional Order ◽  
Nonsmooth Analysis ◽  
State Feedback ◽  
Direct Method ◽  
Young Inequality ◽  
State Feedback Control ◽  
Feedback Controllers ◽  
Theoretical Results

This paper addresses the synchronization issue for the drive-response fractional-order memristor‐based neural networks (FOMNNs) via state feedback control. To achieve the synchronization for considered drive-response FOMNNs, two feedback controllers are introduced. Then, by adopting nonsmooth analysis, fractional Lyapunov’s direct method, Young inequality, and fractional-order differential inclusions, several algebraic sufficient criteria are obtained for guaranteeing the synchronization of the drive-response FOMNNs. Lastly, for illustrating the effectiveness of the obtained theoretical results, an example is given.

Sign in / Sign up

Export Citation Format

Share Document