LMI-Based Stability of Nonlinear Non-Autonomous Fractional-Order Systems With Multiple Time Delays

Zhang, Shuo; Liu, Lu; Cui, Xinshu

doi:10.1109/access.2019.2891732

Cited by 11 publications

(6 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Based on the good characteristics of fractional derivatives, the introduction of fractional derivatives into neural network model has natural advantages. The fractional-order neural network system can overcome the limitations of the integer-order neural network system and describe the characteristics of neurons more accurately [22]- [26]. In recent years, the multistability of fractional-order recurrent neural networks has also attracted the attention of scholars [27], [28].…”

Section: At Present Coexistence and Multistability Of Equilibria Havementioning

confidence: 99%

Multistability of Fractional-Order Recurrent Neural Networks With Discontinuous and Nonmonotonic Activation Functions

et al. 2019

View full text Add to dashboard Cite

The coexistence of multiple stable equilibria in recurrent neural networks is an important dynamic characteristic for associative memory and other applications. In this paper, the existence and local Mittag-Leffler stability of multiple equilibria are investigated for a class of fractional-order recurrent neural networks with discontinuous and nonmonotonic activation functions. By using Brouwer s fixed point theory, several conditions are established to ensure the existence of 5 n equilibria, in which all the components of 4 n equilibria are located in the continuous intervals of the activation functions. and some of the components of 5 n − 4 n equilibria are located at some discontinuous points of the activation functions. The introduction of discontinuous activation functions makes the neural networks have more equilibria than those with continuous activation functions. Furthermore, some criteria are proposed to ensure local Mittag-Leffler stability of 3 n equilibria. The introduction of nonmonotonic activation functions makes the neural networks have more stable equilibria than those with monotonic activation functions. Two examples are given to illustrate the effectiveness of the results. INDEX TERMS Fractional-order recurrent neural network, discontinuous and nonmonotonic activation function, equilibrium point, local Mittag-Leffler stability.

show abstract

Section: At Present Coexistence and Multistability Of Equilibria Havementioning

confidence: 99%

Multistability of Fractional-Order Recurrent Neural Networks With Discontinuous and Nonmonotonic Activation Functions

et al. 2019

View full text Add to dashboard Cite

show abstract

“…For the state estimation problem of the fractional order memory neural networks with leakage and time delay, an efficient estimator is constructed, which makes the corresponding estimation error state globally stable 11 . A class of stability conditions for controlling the nonautonomous fractional order systems with multiple delays are proposed by Zhang et al 12 Besides, for the asymptotic stabilization of fractional order nonlinear systems with multiple delays, two control methods based on Lyapunov‐like function and vector Lyapunov function are proposed respectively 13 . In addition to the fixed time delay, there are also time‐varying and distributed delays.…”

Section: Introductionmentioning

confidence: 99%

Robust control for uncertain variable fractional order differential systems considering time‐varying delays and nonlinear perturbations

Wang

Zhou

Shi

et al. 2022

Optim Control Appl Methods

View full text Add to dashboard Cite

The robust control for uncertain variable fractional order time‐varying delayed differential systems with nonlinear perturbations are concerned in this article. Firstly, by introducing a novel form of the control law which is inspired by the sliding mode design, a new state feedback controller is built. Besides, a specific and comprehensive Lyapunov–Krasovskii function is adopted to deduce the sufficient conditions for the stability and robust stabilization of the system by using some linear matrix inequalities. In addition, the controller gain matrix can also be derived from the point of stability. Finally, two comparison examples are presented to demonstrate the effectiveness of the proposed control technique. The simulation results show that this method can make the state variables converge to the steady ones more quickly and stably.

show abstract

“…Therefore, it is necessary to study FO systems with time delay. Time delays are divided into constant time delays (Hu et al (2020); Nagamani et al (2020); Shafiya et al (2022); Udhayakumar et al (2017); Zhang et al (2019)), discrete and distributed delays (Zhang et al (2018)), and time-varying delays. Time-varying delay is a hot topic in recent years, some scholars have linked it to FO systems.…”

Section: Introductionmentioning

confidence: 99%

Delay-dependent and order-dependent stability and stabilization analysis of variable fractional order uncertain differential systems with time-varying delay via linear matrix inequality approach

Wang

Zhou

Shi

et al. 2022

Journal of Vibration and Control

View full text Add to dashboard Cite

This paper concentrates on the robust stability and stabilization analysis of variable fractional order uncertain differential systems with time-varying delay. Firstly, by using a suitable Lyapunov–Krasovskii function and constructing an appropriate variable fractional order inequality, a novel delay-dependent and order-dependent stability theorem of the nominal systems is proposed. Then, based on the above stability conditions, the robust delay-dependent and order-dependent stability conditions for the uncertain systems are discussed. Moreover, in order to stabilize the nominal and uncertain systems, state feedback controllers are also derived with the help of the presented stability criteria. All the results are in the form of linear matrix inequalities. Finally, two numerical examples are provided to verify the effectiveness of the introduced theoretical formulation.

show abstract

LMI-Based Stability of Nonlinear Non-Autonomous Fractional-Order Systems With Multiple Time Delays

Cited by 11 publications

References 22 publications

Multistability of Fractional-Order Recurrent Neural Networks With Discontinuous and Nonmonotonic Activation Functions

Multistability of Fractional-Order Recurrent Neural Networks With Discontinuous and Nonmonotonic Activation Functions

Robust control for uncertain variable fractional order differential systems considering time‐varying delays and nonlinear perturbations

Delay-dependent and order-dependent stability and stabilization analysis of variable fractional order uncertain differential systems with time-varying delay via linear matrix inequality approach

Contact Info

Product

Resources

About