scholarly journals Hybrid Feedback Control for Exponential Stability and Robust H∞ Control of a Class of Uncertain Neural Network with Mixed Interval and Distributed Time-Varying Delays

Computation ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 62
Author(s):  
Charuwat Chantawat ◽  
Thongchai Botmart ◽  
Rattaporn Supama ◽  
Wajaree Weera ◽  
Sakda Noinang
Keyword(s):  
Neural Network ◽  
Feedback Control ◽  
Exponential Stability ◽  
Convex Combination ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Robust Exponential Stability ◽  
Attenuation Level ◽  
Delay Dependent

This paper is concerned the problem of robust H∞ control for uncertain neural networks with mixed time-varying delays comprising different interval and distributed time-varying delays via hybrid feedback control. The interval and distributed time-varying delays are not necessary to be differentiable. The main purpose of this research is to estimate robust exponential stability of uncertain neural network with H∞ performance attenuation level γ. The key features of the approach include the introduction of a new Lyapunov–Krasovskii functional (LKF) with triple integral terms, the employment of a tighter bounding technique, some slack matrices and newly introduced convex combination condition in the calculation, improved delay-dependent sufficient conditions for the robust H∞ control with exponential stability of the system are obtained in terms of linear matrix inequalities (LMIs). The results of this paper complement the previously known ones. Finally, a numerical example is presented to show the effectiveness of the proposed methods.

DELAY-DEPENDENT ROBUST EXPONENTIAL STABILITY FOR UNCERTAIN RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS

2007 ◽  
Vol 17 (03) ◽  
pp. 207-218 ◽  
Author(s):  
BAOYONG ZHANG ◽  
SHENGYUAN XU ◽  
YONGMIN LI
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
Neuron Activation ◽  
Exponentially Stable

This paper considers the problem of robust exponential stability for a class of recurrent neural networks with time-varying delays and parameter uncertainties. The time delays are not necessarily differentiable and the uncertainties are assumed to be time-varying but norm-bounded. Sufficient conditions, which guarantee that the concerned uncertain delayed neural network is robustly, globally, exponentially stable for all admissible parameter uncertainties, are obtained under a weak assumption on the neuron activation functions. These conditions are dependent on the size of the time delay and expressed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed stability results.

NOVEL STABILITY CRITERIA ON DISCRETE-TIME NEURAL NETWORKS WITH BOTH TIME-VARYING AND DISTRIBUTED DELAYS

2009 ◽  
Vol 19 (04) ◽  
pp. 269-283 ◽  
Author(s):  
TAO LI ◽  
AIGUO SONG ◽  
SHUMIN FEI
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Convex Combination ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Robust Exponential Stability ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Combination Methods

This paper investigates robust exponential stability for discrete-time recurrent neural networks with both time-varying delay (0 ≤ τm ≤ τ(k) ≤ τM) and distributed one. Through partitioning delay intervals [0,τm] and [τm,τM], respectively, and choosing an augmented Lyapunov-Krasovskii functional, the delay-dependent sufficient conditions are obtained by using free-weighting matrix and convex combination methods. These criteria are presented in terms of linear matrix inequalities (LMIs) and their feasibility can be easily checked by resorting to LMI in Matlab Toolbox in Ref. 1. The activation functions are not required to be differentiable or strictly monotonic, which generalizes those earlier forms. As an extension, we further consider the robust stability of discrete-time delayed Cohen-Grossberg neural networks. Finally, the effectiveness of the proposed results is further illustrated by three numerical examples in comparison with the reported ones.

scholarly journals Robust Exponential Stability for LPD Discrete-Time System with Interval Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Kanit Mukdasai
Keyword(s):  
Exponential Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Robust Exponential Stability ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the problem of robust exponential stability for uncertain linear-parameter dependent (LPD) discrete-time system with delay. The delay is of an interval type, which means that both lower and upper bounds for the time-varying delay are available. The uncertainty under consideration is norm-bounded uncertainty. Based on combination of the linear matrix inequality (LMI) technique and the use of suitable Lyapunov-Krasovskii functional, new sufficient conditions for the robust exponential stability are obtained in terms of LMI. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

Global Robust Exponential Stability of Cohen-Grossberg Neural Network with Time Varying Delays

2012 ◽  
Vol 182-183 ◽  
pp. 1135-1140 ◽  
Author(s):  
Rui Zhang ◽  
Chang Tao Wang
Keyword(s):  
Neural Network ◽  
Exponential Stability ◽  
Functional Method ◽  
Jensen Inequality ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
Inequality Technique ◽  
Global Robust Exponential Stability

In this paper, the global robust exponential stability is discussed for Cohen-Grossgerg neural network with parameter uncertainties and time varying delays. On the basis of the linear matrix inequalities (LMIs) technique, and Lyapunov functional method combined with the Bellman inequality and Jensen inequality technique, we have obtained the main condition to ensure the global robust exponential stability of the equilibrium point for this system. The proposed result is less restrictive, easier to check in practice. Remarks are made with other previous works to show the superiority of the obtained result, and the simulation example is used to demonstrate the effectiveness of our result.

scholarly journals Delay-Dependent Robust Exponential Stability for Uncertain Neutral Stochastic Systems with Interval Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Weihua Mao ◽  
Feiqi Deng ◽  
Anhua Wan
Keyword(s):  
Exponential Stability ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Mean Square ◽  
Robust Exponential Stability ◽  
Interval Time ◽  
Time Varying Delay ◽  
Mean Square Exponential Stability ◽  
Delay Dependent

This paper discusses the mean-square exponential stability of uncertain neutral linear stochastic systems with interval time-varying delays. A new augmented Lyapunov-Krasovskii functional (LKF) has been constructed to derive improved delay-dependent robust mean-square exponential stability criteria, which are forms of linear matrix inequalities (LMIs). By free-weight matrices method, the usual restriction that the stability conditions only bear slow-varying derivative of the delay is removed. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.

scholarly journals New Robust Exponential Stability Criterion for Uncertain Neutral Systems with Discrete and Distributed Time-Varying Delays and Nonlinear Perturbations

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Sirada Pinjai ◽  
Kanit Mukdasai
Keyword(s):  
Exponential Stability ◽  
Model Transformation ◽  
Sufficient Conditions ◽  
Coefficient Matrix ◽  
Linear Matrix ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Matrix Inequalities ◽  
Neutral Systems ◽  
Robust Exponential Stability

We investigate the problem of robust exponential stability for uncertain neutral systems with discrete and distributed time-varying delays and nonlinear perturbations. Based on the combination of descriptor model transformation, decomposition technique of coefficient matrix, and utilization of zero equation and new Lyapunov functional, sufficient conditions for robust exponential stability are obtained and formulated in terms of linear matrix inequalities (LMIs). The new stability conditions are less conservative and more general than some existing results.

Global Robust Exponential Stability of Interval Cohen-Grossberg Neural Network with Time Varying Delays

2013 ◽  
Vol 756-759 ◽  
pp. 3884-3888 ◽  
Author(s):  
Rui Zhang ◽  
Jian Liu ◽  
Meng Xin Li ◽  
Mei Ju Liu
Keyword(s):  
Neural Network ◽  
Exponential Stability ◽  
Functional Method ◽  
Jensen Inequality ◽  
Linear Matrix ◽  
Fast Time ◽  
Time Varying ◽  
Robust Exponential Stability ◽  
Inequality Technique ◽  
Global Robust Exponential Stability

In this paper, the global robust exponential stability is discussed for interval Cohen-Grossgerg neural network with time varying delays. On the basis of the linear matrix inequalities (LMIs) technique, and Lyapunov functional method combined with the Bellman inequality and Jensen inequality technique, we have obtained the main condition to ensure the global robust exponential stability of the equilibrium point for this system. The obtained stability criterion is dependent on the upper bound of time varying delays. The proposed result is less restrictive, and suitable of the cases of slow or fast time varying delays, easier to check in practice. Remarks are made with other previous works to show the superiority of the obtained result, and the simulation example is used to demonstrate the effectiveness of our result.

ROBUST EXPONENTIAL STABILITY OF STOCHASTIC TIME-DELAY SYSTEMS WITH UNCERTAINTIES AND NONLINEAR PERTURBATIONS

2009 ◽  
Vol 06 (01) ◽  
pp. 61-71 ◽  
Author(s):  
HUAICHENG YAN ◽  
MAX Q.-H. MENG ◽  
XINHAN HUANG ◽  
HAO ZHANG
Keyword(s):  
Exponential Stability ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Linear Matrix ◽  
Mean Square ◽  
Nonlinear Perturbations ◽  
Robust Exponential Stability ◽  
Mean Square Stability ◽  
Delay Dependent

In this paper, the delay-dependent robust exponential mean-square stability analysis problem is considered for a class of uncertain stochastic systems with time-varying delay and nonlinear perturbations. Some sufficient conditions on delay-dependent robust exponential stability in the mean square are established in terms of linear matrix inequalities (LMIs) by exploiting a novel Lyapunov–Krasovskii functional and by making use of zero equations methods. These developed results indicate less conservatism than the existing ones due to the introduction of some free weighting matrices which can be selected properly. The new delay-dependent stability criteria are expressed as a set of LMIs, which can be readily solved by using standard numerical software. Numerical examples are provided to demonstrate the effectiveness and the applicability of the proposed criteria.

scholarly journals Observer-Based Robust Control Method for Switched Neutral Systems in the Presence of Interval Time-Varying Delays

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2473
Author(s):  
Hamid Ghadiri ◽  
Hamed Khodadadi ◽  
Saleh Mobayen ◽  
Jihad H. Asad ◽  
Thaned Rojsiraphisal ◽  
...  
Keyword(s):  
Exponential Stability ◽  
Control Method ◽  
Sufficient Conditions ◽  
Control Technique ◽  
Function Technique ◽  
Linear Matrix ◽  
Time Varying ◽  
Neutral Systems ◽  
Robust Exponential Stability ◽  
Switched Neutral Systems

In this study, the challenges of the controller design of a class of Uncertain Switched Neutral Systems (USNSs) in the presence of discrete, neutral, and time-varying delays are considered by using a robust observer-based control technique. The cases where the uncertainties are normbounded and time-varying are emphasized in this research. The adopted control approach reduces the prescribed level of disturbance input on the controlled output in the closed-loop form and the robust exponential stability of the control system. The challenge of parametric uncertainty in USNSs is solved by designing a robust output observer-based control and applying the Yakubovich lemma. Since the separation principle does not generally hold in this research, the controller and observer cannot be designed separately, sufficient conditions are suggested. These conditions are composed of applying the average dwell time approach and piecewise Lyapunov function technique in terms of linear matrix inequalities, which guarantees robust exponential stability of the observer-based output controller. Finally, two examples are given to determine the effectiveness of the proposed method.

scholarly journals Sufficient Conditions on the Exponential Stability of Neutral Stochastic Differential Equations with Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Yanwei Tian ◽  
Baofeng Chen
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Stochastic Differential Equations ◽  
Lyapunov Stability ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Delay Dependent

The exponential stability is investigated for neutral stochastic differential equations with time-varying delays. Based on the Lyapunov stability theory and linear matrix inequalities (LMIs) technique, some delay-dependent criteria are established to guarantee the exponential stability in almost sure sense. Finally a numerical example is provided to illustrate the feasibility of the result.

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