scholarly journals The Lyapunov-Razumikhin theorem for the conformable fractional system with delay

2021 ◽  
Vol 7 (3) ◽  
pp. 4795-4802
Author(s):  
Narongrit Kaewbanjak ◽  
◽  
Watcharin Chartbupapan ◽  
Kamsing Nonlaopon ◽  
Kanit Mukdasai ◽  
...  
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Functional ◽  
Stability Theorem ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Uniform Asymptotic Stability ◽  
Razumikhin Theorem ◽  
System With Delay ◽  
Fractional System ◽  
Delay Dependent

<abstract><p>This paper explicates the Razumikhin-type uniform stability and a uniform asymptotic stability theorem for the conformable fractional system with delay. Based on a Razumikhin-Lyapunov functional and some inequalities, a delay-dependent asymptotic stability criterion is in the term of a linear matrix inequality (LMI) for the conformable fractional linear system with delay. Moreover, an application of our theorem is illustrated via a numerical example.</p></abstract>

Delay-Dependent Asymptotical Stabilization Criterion of Recurrent Neural Networks

2013 ◽  
Vol 330 ◽  
pp. 1045-1048 ◽  
Author(s):  
Grienggrai Rajchakit
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Lyapunov Functional ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Weighting Matrix ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper deals with the problem of delay-dependent stability criterion of discrete-time recurrent neural networks with time-varying delays. Based on quadratic Lyapunov functional approach and free-weighting matrix approach, some linear matrix inequality criteria are found to guarantee delay-dependent asymptotical stability of these systems. And one example illustrates the exactness of the proposed criteria.

DELAY-DEPENDENT ASYMPTOTIC STABILITY OF NEURAL NETWORKS WITH TIME-VARYING DELAYS

2008 ◽  
Vol 18 (01) ◽  
pp. 245-250 ◽  
Author(s):  
SHENGYUAN XU ◽  
JAMES LAM ◽  
DANIEL W. C. HO
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Asymptotic Stability ◽  
Stability Condition ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Unique Equilibrium ◽  
Delay Dependent ◽  
Asymptotic Stability Condition

This paper considers the problem of stability analysis for neural networks with time-varying delays. The time-varying delays under consideration are assumed to be bounded but not necessarily differentiable. In terms of a linear matrix inequality, a delay-dependent asymptotic stability condition is developed, which ensures the existence of a unique equilibrium point and its global asymptotic stability. The proposed stability condition is easy to check and less conservative. An example is provided to show the effectiveness of the proposed condition.

scholarly journals Delay-Dependent Exponential Stability for Discrete-Time BAM Neural Networks with Time-Varying Delays

2008 ◽  
Vol 2008 ◽  
pp. 1-14 ◽  
Author(s):  
Yonggang Chen ◽  
Weiping Bi ◽  
Yuanyuan Wu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Discrete Time ◽  
Lyapunov Functional ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Bam Neural Networks ◽  
Delay Dependent ◽  
Slack Matrices

This paper considers the delay-dependent exponential stability for discrete-time BAM neural networks with time-varying delays. By constructing the new Lyapunov functional, the improved delay-dependent exponential stability criterion is derived in terms of linear matrix inequality (LMI). Moreover, in order to reduce the conservativeness, some slack matrices are introduced in this paper. Two numerical examples are presented to show the effectiveness and less conservativeness of the proposed method.

IMPULSIVE EFFECTS ON STABILITY OF A CLASS OF NONLINEAR NEURAL NETWORKS WITH MULTIPLE DELAYS

2009 ◽  
Vol 19 (09) ◽  
pp. 3143-3148
Author(s):  
QINGHUA ZHOU ◽  
LI WAN ◽  
QUNJIAO ZHANG
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Linear Matrix ◽  
Multiple Delays ◽  
Lyapunov Functionals ◽  
Matrix Inequality ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Stability Results ◽  
Nonlinear Neural Networks

The global asymptotic stability (GAS) for a class of nonlinear impulsive neural networks with multiple delays are discussed. By skillfully constructing suitable Lyapunov functionals and the linear matrix inequality (LMI) technique, a new sufficient delay-dependent stability criterion is derived. The proposed stability results are less conservative than some recently known ones in the literature, which is demonstrated via two examples with simulation.

scholarly journals The Asymptotic Synchronization Analysis for Two Kinds of Complex Dynamical Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Ze Tang ◽  
Jianwen Feng
Keyword(s):  
Time Delay ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
Complex Dynamical Networks ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Dynamical Networks ◽  
Simulation Results ◽  
Delay Dependent ◽  
Asymptotic Synchronization

We consider a class of complex networks with both delayed and nondelayed coupling. In particular, we consider the situation for both time delay-independent and time delay-dependent complex dynamical networks and obtain sufficient conditions for their asymptotic synchronization by using the Lyapunov-Krasovskii stability theorem and the linear matrix inequality (LMI). We also present some simulation results to support the validity of the theories.

ANALYSIS ON GLOBAL STABILITY OF STOCHASTIC NEURAL NETWORKS OF NEUTRAL TYPE

2008 ◽  
Vol 22 (32) ◽  
pp. 3159-3170 ◽  
Author(s):  
JU H. PARK ◽  
O. M. KWON
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Lyapunov Stability ◽  
Neutral Type ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Matrix Inequality ◽  
Delay Dependent ◽  
Delay Dependent Stability

In this paper, the problem of global asymptotic stability of stochastic neural networks of neutral type is considered. Based on the Lyapunov stability theory, a new delay-dependent stability criterion for the network is derived in terms of LMI (linear matrix inequality). A numerical example is given to show the effectiveness of the proposed method.

scholarly journals Global Dissipativity on Uncertain Discrete-Time Neural Networks with Time-Varying Delays

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Qiankun Song ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Computationally Efficient ◽  
Inequality Technique ◽  
General Activation ◽  
Delay Dependent

The problems on global dissipativity and global exponential dissipativity are investigated for uncertain discrete-time neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing linear matrix inequality technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Illustrated examples are given to show the effectiveness of the proposed criteria. It is noteworthy that because neither model transformation nor free-weighting matrices are employed to deal with cross terms in the derivation of the dissipativity criteria, the obtained results are less conservative and more computationally efficient.

DELAY-DEPENDENT GLOBAL ROBUST ASYMPTOTIC STABILITY ANALYSIS OF BAM NEURAL NETWORKS WITH TIME DELAY: AN LMI APPROACH

2007 ◽  
Vol 03 (01) ◽  
pp. 57-68 ◽  
Author(s):  
XU-YANG LOU ◽  
BAO-TONG CUI
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Lmi Approach ◽  
Global Robust Asymptotic Stability ◽  
Dependent Property ◽  
Delay Dependent ◽  
Robust Asymptotic Stability

The global robust asymptotic stability of bi-directional associative memory (BAM) neural networks with constant or time-varying delays is studied. An approach combining the Lyapunov-Krasovskii functional with the linear matrix inequality (LMI) is taken to study the problem. Some a criteria for the global robust asymptotic stability, which gives information on the delay-dependent property, are derived. Some illustrative examples are given to demonstrate the effectiveness of the obtained results.

scholarly journals A Novel Delay-Dependent Asymptotic Stability Conditions for Differential and Riemann-Liouville Fractional Differential Neutral Systems with Constant Delays and Nonlinear Perturbation

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 82 ◽  
Author(s):  
Watcharin Chartbupapan ◽  
Ovidiu Bagdasar ◽  
Kanit Mukdasai
Keyword(s):  
Asymptotic Stability ◽  
Stability Criterion ◽  
Nonlinear Perturbation ◽  
Linear Matrix ◽  
Neutral System ◽  
The Novel ◽  
Neutral Systems ◽  
Fractional Differential ◽  
Delay Dependent ◽  
Single Constant

The novel delay-dependent asymptotic stability of a differential and Riemann-Liouville fractional differential neutral system with constant delays and nonlinear perturbation is studied. We describe the new asymptotic stability criterion in the form of linear matrix inequalities (LMIs), using the application of zero equations, model transformation and other inequalities. Then we show the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with constant delays. Furthermore, we not only present the improved delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with single constant delay but also the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral equation with constant delays. Numerical examples are exploited to represent the improvement and capability of results over another research as compared with the least upper bounds of delay and nonlinear perturbation.

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