scholarly journals Stability Analysis for Uncertain Neural Networks of Neutral Type with Time-Varying Delay in the Leakage Term and Distributed Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Qi Zhou ◽  
Xueying Shao ◽  
Jin Zhu ◽  
Hamid Reza Karimi
Keyword(s):  
Neutral Type ◽  
Distributed Delay ◽  
Linear Matrix ◽  
Time Varying ◽  
Leakage Term ◽  
Time Varying Delay ◽  
The Stability ◽  
Uncertain Networks ◽  
Varying Delay ◽  
Stability Results

The stability problem is investigated for a class of uncertain networks of neutral type with leakage, time-varying discrete, and distributed delays. Both the parameter uncertainty and the generalized activation functions are considered in this paper. New stability results are achieved by constructing an appropriate Lyapunov-Krasovskii functional and employing the free weighting matrices and the linear matrix inequality (LMI) method. Some numerical examples are given to show the effectiveness and less conservatism of the proposed results.

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

scholarly journals Improved Stability Criteria of Static Recurrent Neural Networks with a Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Lei Ding ◽  
Hong-Bing Zeng ◽  
Wei Wang ◽  
Fei Yu
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Improved Stability ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper investigates the stability of static recurrent neural networks (SRNNs) with a time-varying delay. Based on the complete delay-decomposing approach and quadratic separation framework, a novel Lyapunov-Krasovskii functional is constructed. By employing a reciprocally convex technique to consider the relationship between the time-varying delay and its varying interval, some improved delay-dependent stability conditions are presented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the merits and the effectiveness of the proposed methods.

scholarly journals Robust Stability of a Class of Uncertain Lur'e Systems of Neutral Type

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
W. Weera ◽  
P. Niamsup
Keyword(s):  
Neutral Type ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Lur’E Systems ◽  
Interval Time ◽  
Delay Function ◽  
Time Varying Delay ◽  
Bounded Nonlinearity ◽  
Varying Delay

This paper deals with the problem of stability for a class of Lur’e systems with interval time-varying delay and sector-bounded nonlinearity. The interval time-varying delay function is not assumed to be differentiable. We analyze the global exponential stability for uncertain neutral and Lur’e dynamical systems with some sector conditions. By constructing a set of improved Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, we establish some stability criteria in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the results.

scholarly journals Stability analysis for neural networks with discrete and leakage time-varying delay systems with delay-range-dependence and delay-derivative-dependence

2021 ◽  
Author(s):  
Pin-Lin Liu
Keyword(s):  
Neural Networks ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Decomposition Approach ◽  
Time Varying Delay ◽  
Systems Model ◽  
The Neural Networks ◽  
The Stability ◽  
Varying Delay

The paper deals with the stability problem of neural networks with discrete and leakage interval time-varying delays. Firstly, a novel Lyapunov-Krasovskii functional was constructed based on the neural networks leakage time-varying delay systems model. The delayed decomposition approach (DDA) and integral inequality techniques (IIA) were altogether employed, which can help to estimate the derivative of Lyapunov-Krasovskii functional and effectively extend the application area of the results. Secondly, by taking the lower and upper bounds of time-delays and their derivatives, a criterion on asymptotical was presented in terms of linear matrix inequality (LMI), which can be easily checked by resorting to LMI in Matlab Toolbox. Thirdly, the resulting criteria can be applied for the case when the delay derivative is lower and upper bounded, when the lower bound is unknown, and when no restrictions are cast upon the derivative characteristics. Finally, through numerical examples, the criteria will be compared with relative ones. The smaller delay upper bound was obtained by the criteria, which demonstrates that our stability criterion can reduce the conservatism more efficiently than those earlier ones.

Improved Results on Stability Criteria for Singular Systems with Interval Time-Varying Delays

2020 ◽  
pp. 2130001
Author(s):  
Chaibi Noreddine ◽  
Belamfedel Alaoui Sadek ◽  
Tissir El Houssaine ◽  
Bensalem Boukili
Keyword(s):  
Singular Systems ◽  
Singular System ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Small Gain ◽  
The Stability ◽  
Varying Delay ◽  
Singular Time

The purpose of this paper is to address the problem of assessing the stability of singular time-varying delay systems. In order to highlight the relations between the delay and the state, the singular system is transformed into a neutral form. Then, a model transformation using a three-terms approximation of the delayed state is exploited. Based on the lifting method and the Lyapunov–Krasovskii functional (LKF) method, a new linear matrix inequality (LMI) is obtained, allowing conclusions on stability to be drawn using the scaled small gain theorem (SSG). The use of SSG theorem for stability of singular systems with time-varying delay has not been investigated elsewhere in the literature. This represents the main novelty of this article. The result is applicable for assessing the stability of both singular systems and neutral systems with time-varying delays. The less conservativeness of the stability test is illustrated by comparison with recent literature results.

scholarly journals New Stability Analysis for Linear Systems with Time-Varying Delay Based on Combined Convex Technique

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Bin Yang ◽  
Chen-xin Fan
Keyword(s):  
Linear Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Integral Term ◽  
Time Varying Delay ◽  
Wirtinger Inequality ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

A novel combined convex method is developed for the stability of linear systems with a time-varying delay. A new delay-dependent stability condition expressed in terms of linear matrix inequalities (LMIs) is derived by employing a dedicated constructed Lyapunov-Krasovskii functional (LKF), utilizing the Wirtinger inequality and the reciprocally convex approach to handle the integral term of quadratic quantities. Different from the previous convex techniques which only tackle the time-varying delay, our method adopts the idea of combined convex technique which can tackle not only the delay but also the delay variation. Four well-known examples are illustrated to show the effectiveness of the proposed results.

scholarly journals Exponential Stabilization of Neutral-Type Neural Networks with Interval Nondifferentiable and Distributed Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
W. Weera ◽  
P. Niamsup
Keyword(s):  
Neural Networks ◽  
Neutral Type ◽  
Exponential Stabilization ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Activation Functions ◽  
Delay Function ◽  
Time Varying Delay ◽  
Varying Delay

The problem of exponential stabilization of neutral-type neural networks with various activation functions and interval nondifferentiable and distributed time-varying delays is considered. The interval time-varying delay function is not required to be differentiable. By employing new and improved Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, the stabilizability criteria are formulated in terms of a linear matrix inequalities. Numerical examples are given to illustrate and show the effectiveness of the obtained results.

scholarly journals Synchronization in Array of Coupled Neural Networks with Unbounded Distributed Delay and Limited Transmission Efficiency

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Xinsong Yang ◽  
Mengzhe Zhou ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Distributed Delay ◽  
Transmission Efficiency ◽  
Functional Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Coupled Neural Networks ◽  
Time Varying Delay ◽  
Unbounded Distributed Delays ◽  
Varying Delay

This paper investigates global synchronization in an array of coupled neural networks with time-varying delays and unbounded distributed delays. In the coupled neural networks, limited transmission efficiency between coupled nodes, which makes the model more practical, is considered. Based on a novel integral inequality and the Lyapunov functional method, sufficient synchronization criteria are derived. The derived synchronization criteria are formulated by linear matrix inequalities (LMIs) and can be easily verified by using Matlab LMI Toolbox. It is displayed that, when some of the transmission efficiencies are limited, the dynamics of the synchronized state are different from those of the isolated node. Furthermore, the transmission efficiency and inner coupling matrices between nodes play important roles in the final synchronized state. The derivative of the time-varying delay can be any given value, and the time-varying delay can be unbounded. The outer-coupling matrices can be symmetric or asymmetric. Numerical simulations are finally given to demonstrate the effectiveness of the theoretical results.

Fuzzy Control of a Class of Discrete-Time Fuzzy Bilinear Systems with Time-Delay

2012 ◽  
Vol 482-484 ◽  
pp. 1881-1885
Author(s):  
Jian Hu Jiang ◽  
Chao Wu ◽  
Yun Wang Ge ◽  
Li Jun Song
Keyword(s):  
Discrete Time ◽  
Sufficient Conditions ◽  
Bilinear System ◽  
Stability Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
The Stability ◽  
Varying Delay

The stability control problem is considered for a class of discrete-time T-S fuzzy bilinear system with time-varying delay in both state and input. Based on the parallel distribute compensation (PDC) scheme, some sufficient conditions are derived to guarantee the global asymptotically stability of the overall fuzzy system, which are represented in terms of matrix inequality. The corresponding controller can be obtained by solving a set of linear matrix inequalities. Finally, a simulation example shows that the approach is effective.

Robust Absolute Stability Criteria for Uncertain Lurie System With Interval Time-Varying Delay

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Pankaj Mukhija ◽  
Indra Narayan Kar ◽  
Rajendra K. P. Bhatt
Keyword(s):  
Absolute Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Interval Time ◽  
Time Varying Delay ◽  
Wirtinger Inequality ◽  
Chua’S Oscillator ◽  
The Stability ◽  
Varying Delay

This paper addresses the problem of absolute stability of Lurie system with interval time-varying delay. The delay range is divided into two equal segments and an appropriate Lyapunov–Krasovskii functional (LKF) is defined. A tighter bounding technique for the derivative of LKF is developed. This bounding technique in combination with the Wirtinger inequality is used to develop the absolute stability criterion in terms of linear matrix inequalities (LMIs). The stability analysis is also extended to the Lurie system with norm-bounded parametric uncertainties. The effectiveness of the proposed approach has been illustrated through a numerical example and Chua's oscillator.

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