NOVEL ROBUST DELAY-DEPENDENT CRITERION FOR ABSOLUTE STABILITY OF LUR'E SYSTEMS OF NEUTRAL TYPE

2009 ◽  
Vol 23 (13) ◽  
pp. 1641-1650 ◽  
Author(s):  
S. M. LEE ◽  
O. M. KWON ◽  
JU H. PARK
Keyword(s):  
Linear Matrix Inequalities ◽  
Lyapunov Functional ◽  
Absolute Stability ◽  
Neutral Type ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Lur’E Systems ◽  
Numerical Examples ◽  
Delay Dependent

This letter considers uncertain Lur'e systems of neutral type with sector and slope restrictions. By constructing a new Lyapunov functional, a novel delay-dependent criterion for absolute stability is derived in terms of linear matrix inequalities (LMIs). Two numerical examples are illustrated to show the effectiveness of the proposed method.

scholarly journals Novel Delay-Decomposing Approaches to Absolute Stability Criteria for Neutral-Type Lur’e Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Liang-Dong Guo ◽  
Sheng-Juan Huang ◽  
Li-Bing Wu
Keyword(s):  
Absolute Stability ◽  
Neutral Type ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Lur’E Systems ◽  
Delay Dependent ◽  
Numerical Complexity ◽  
Variation Interval

The problem of absolute stability analysis for neutral-type Lur’e systems with time-varying delays is investigated. Novel delay-decomposing approaches are proposed to divide the variation interval of the delay into three unequal subintervals. Some new augment Lyapunov–Krasovskii functionals (LKFs) are defined on the obtained subintervals. The integral inequality method and the reciprocally convex technique are utilized to deal with the derivative of the LKFs. Several improved delay-dependent criteria are derived in terms of the linear matrix inequalities (LMIs). Compared with some previous criteria, the proposed ones give the results with less conservatism and lower numerical complexity. Two numerical examples are included to illustrate the effectiveness and the improvement of the proposed method.

Delayed-Decomposition Approach for Absolute Stability of Neutral-Type Lurie Control Systems With Time-Varying Delays

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Pin-Lin Liu
Keyword(s):  
Control Systems ◽  
Lyapunov Functional ◽  
Absolute Stability ◽  
Neutral Type ◽  
Upper Bounds ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Decomposition Approach ◽  
Delay Dependent

The problem of absolute stability for a class of neutral-type Lurie control system with nonlinearity located in an infinite sector and in a finite one is investigated in this paper. Based on the delayed-decomposition approach (DDA), a new augmented Lyapunov functional is constructed and the delay dependent conditions for asymptotic stability are derived by applying an integral inequality approach (IIA) in terms of linear matrix inequalities (LMIs). Finally, numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.

MASTER–SLAVE SYNCHRONIZATION OF LUR'E SYSTEMS WITH GENERAL SECTOR-BOUNDED NONLINEARITIES

2009 ◽  
Vol 19 (02) ◽  
pp. 517-529 ◽  
Author(s):  
QING-LONG HAN ◽  
DRISS MEHDI ◽  
DONGSHENG HAN
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequalities ◽  
Lyapunov Functional ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Lur’E Systems ◽  
Sector Condition ◽  
Special Cases ◽  
Delay Feedback Control ◽  
Delay Dependent

This paper deals with master–slave synchronization for Lur'e systems subject to a more general sector condition by using time delay feedback control. A new Lyapunov–Krasovskii functional and a new Lur'e–Postnikov Lyapunov functional are proposed to obtain some new delay-dependent synchronization criteria, which are formulated in the form of linear matrix inequalities (LMIs). These criteria cover some existing results as their special cases. An example shows that the result derived in this paper significantly improves some existing ones.

scholarly journals New Results on Stability Analysis of Uncertain Neutral-Type Lur’e Systems Derived from a Modified Lyapunov-Krasovskii Functional

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-20 ◽  
Author(s):  
Wenyong Duan ◽  
Yan Li ◽  
Jian Chen ◽  
Lin Jiang
Keyword(s):  
Absolute Stability ◽  
Neutral Type ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
Lur’E Systems ◽  
Numerical Examples ◽  
Lur’E System ◽  
Delay Dependent

This paper is concerned with the problem of the absolute and robustly absolute stability for the uncertain neutral-type Lur’e system with time-varying delays. By introducing a modified Lyapunov-Krasovskii functional (LKF) related to a delay-product-type function and two delay-dependent matrices, some new delay-dependent robustly absolute stability criteria are proposed, which can be expressed as convex linear matrix inequality (LMI) framework. The criteria proposed in this paper are less conservative than some recent previous ones. Finally, some numerical examples are presented to show the effectiveness of the proposed approach.

scholarly journals A New Stability Criterion for Systems with Distributed Time-Varying Delays via Mixed Inequalities Method

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Jun-kang Tian ◽  
Yan-min Liu
Keyword(s):  
Linear Matrix Inequalities ◽  
Stability Criterion ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
New Inequalities

This paper is concerned with the delay-dependent stability of systems with distributed time-varying delays. The novelty relies on the use of some new inequalities which are less conservative than some existing inequalities. A less conservative stability criterion is obtained by constructing some new augmented Lyapunov–Krasovskii functionals, which are given in terms of linear matrix inequalities. The effectiveness of the presented criterion is demonstrated by two numerical examples.

scholarly journals Novel Stability Analysis for Uncertain Neutral-Type Lur’e Systems with Time-Varying Delays Using New Inequality

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Yanmeng Wang ◽  
Lianglin Xiong ◽  
Yongkun Li ◽  
Haiyang Zhang ◽  
Chen Peng
Keyword(s):  
Stability Analysis ◽  
Neutral Type ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Lur’E Systems ◽  
New Class ◽  
Inequality Techniques ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper considers the delay-dependent stability analysis of neutral-type Lur’e systems with time-varying delays and sector bounded nonlinearities. First of all, using constructed function methods, a new Jensen-like inequality is introduced to obtain less conservative results. Second, a new class of Lyapunov-Krasovskii functional (LKF) is constructed according to the characteristic of the considered systems. Third, combining with the new inequality and reciprocal convex approach and some other inequality techniques, the new less conservative robust stability criteria are shown in the form of linear matrix inequalities (LMIs). Finally, three examples demonstrate the feasibility and the superiority of our methods.

scholarly journals New Results on Passivity for Discrete-Time Stochastic Neural Networks with Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Wei Kang ◽  
Jun Cheng ◽  
Xiangyang Cheng
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Passivity Analysis ◽  
Delay Dependent

The problem of passivity analysis for discrete-time stochastic neural networks with time-varying delays is investigated in this paper. New delay-dependent passivity conditions are obtained in terms of linear matrix inequalities. Less conservative conditions are obtained by using integral inequalities to aid in the achievement of criteria ensuring the positiveness of the Lyapunov-Krasovskii functional. At last, numerical examples are given to show the effectiveness of the proposed method.

IMPROVED RESULTS ON STABILITY ANALYSIS OF NEURAL NETWORKS WITH TIME-VARYING DELAYS: NOVEL DELAY-DEPENDENT CRITERIA

2010 ◽  
Vol 24 (08) ◽  
pp. 775-789 ◽  
Author(s):  
O. M. KWON ◽  
S. M. LEE ◽  
JU H. PARK
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Lyapunov Functional ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Analysis Techniques ◽  
The Neural Networks ◽  
Delay Dependent

In this paper, the problem of stability analysis of neural networks with discrete time-varying delays is considered. By constructing a new Lyapunov functional and some novel analysis techniques, new delay-dependent criteria for checking the asymptotic stability of the neural networks are established. The criteria are presented in terms of linear matrix inequalities, which can be easily solved and checked by various convex optimization algorithms. Three numerical examples are included to show the superiority of our results.

scholarly journals Passivity and Synchronization of Multiple Multi-Delayed Neural Networks via Impulsive Control

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yong Wang ◽  
Zhichun Yang ◽  
Tonglai Liu ◽  
Hong-An Tang
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequalities ◽  
Lyapunov Functional ◽  
Impulsive Control ◽  
Time Dependent ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Delayed Neural Networks ◽  
Theoretical Results

This paper is concerned with the passivity and synchronization for multiple multi-delayed neural networks (MMDNNs) under impulsive control. To ensure the passivity, input strict passivity, and output strict passivity in MMDNNs, a suitable impulsive controller is designed. Moreover, an impulsive time-dependent Lyapunov functional is exploited to obtain the synchronization criterion of MMDNNs, where the criterion is formulated by linear matrix inequalities. Numerical examples are given to verify the validity of the theoretical results.

scholarly journals New Absolute Stability Conditions of Lur’e Systems with Time-Varying Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Wei Wang ◽  
Hong-Bing Zeng
Keyword(s):  
Absolute Stability ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Lur’E Systems ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
The Relationship ◽  
Varying Delay

This paper is focused on the absolute stability of Lur’e systems with time-varying delay. Based on the quadratic separation framework, a complete delay-decomposing Lyapunov-Krasovskii functional is constructed. By considering the relationship between the time-varying delay and its varying interval, improved delay-dependent absolute stability conditions in terms of linear matrix inequalities (LMIs) are obtained. Moreover, the derived conditions are extended to systems with time-varying structured uncertainties. Finally, a numerical example is given to show the advantage over existing literatures.

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