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.

A Novel Stability Criterion of Lur’e Systems with Time-Varying Delay Based on Relaxed Conditions

2018 ◽  
Vol 30 (6) ◽  
pp. 965-970
Author(s):  
Peng Zhang ◽  
◽  
Pitao Wang ◽  
Tao Shen
Keyword(s):  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Lur’E Systems ◽  
Decomposition Approach ◽  
Time Varying Delay ◽  
Delay Decomposition Approach ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper considers the absolute stability for Lur’e systems with time-varying delay and sector-bounded nonlinear. In this paper, a new relaxed condition based on delay decomposition approach is proposed. By using this technique and employing some inequality, the new delay-dependent stability criteria for Lur’e systems are derived in the form of linear matrix inequalities (LMIs). A numerical example is presented to show less conservatism of proposed methods compared with the previous.

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 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.

Further Results on Exponential Robust Stability Analysis for Recurrent Neural Networks With Time-Varying Delay

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Pin-Lin Liu
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Time Varying ◽  
Robust Exponential Stability ◽  
Time Varying Delay ◽  
Robust Stability Analysis ◽  
The Relationship ◽  
Varying Delay

In this paper, the problems of determining the robust exponential stability and estimating the exponential convergence rate for recurrent neural networks (RNNs) with parametric uncertainties and time-varying delay are studied. The relationship among the time-varying delay, its upper bound, and their difference is taken into account. The developed stability conditions are in terms of linear matrix inequalities (LMIs) and the integral inequality approach (IIA), which can be checked easily by recently developed algorithms solving LMIs. Furthermore, the proposed stability conditions are less conservative than some recently known ones in the literature, and this has been demonstrated via four examples with simulation.

New Delay-Dependent Stability Criteria for Systems with Interval Time-Varying Delay

2011 ◽  
Vol 48-49 ◽  
pp. 734-739 ◽  
Author(s):  
Dong Sheng Xu ◽  
Jun Kang Tian
Keyword(s):  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Integral Term ◽  
Interval Time ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper is concerned with delay-dependent stability for systems with interval time varying delay. By defining a new Lyapunov functional which contains a triple-integral term with the idea of decomposing the delay interval of time-varying delay, an improved criterion of asymptotic stability is derived in term of linear matrix inequalities. The criterion proves to be less conservative with fewer matrix variables than some previous ones. Finally, a numerical example is given to show the effectiveness of the proposed method.

scholarly journals Stochastic Passivity of Uncertain Neural Networks with Time-Varying Delays

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
Jianting Zhou ◽  
Qiankun Song ◽  
Jianxi Yang
Keyword(s):  
Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Analysis Technique ◽  
Uncertain Neural Networks ◽  
Delay Dependent ◽  
Varying Delay

The passivity problem is investigated for a class of stochastic uncertain neural networks with time-varying delay as well as generalized activation functions. By constructing appropriate Lyapunov-Krasovskii functionals, and employing Newton-Leibniz formulation, the free-weighting matrix method, and stochastic analysis technique, a delay-dependent criterion for checking the passivity of the addressed neural networks is established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. An example with simulation is given to show the effectiveness and less conservatism of the proposed criterion. It is noteworthy that the traditional assumptions on the differentiability of the time-varying delays and the boundedness of its derivative are removed.

MASTER-SLAVE SYNCHRONIZATION OF LUR'E SYSTEMS BASED ON TIME-VARYING DELAY FEEDBACK CONTROL

2007 ◽  
Vol 17 (11) ◽  
pp. 4159-4166 ◽  
Author(s):  
HE HUANG ◽  
JINDE CAO
Keyword(s):  
Feedback Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Lur’E Systems ◽  
Time Varying Delay ◽  
Synchronization Problem ◽  
Master System ◽  
Delay Feedback Control ◽  
Delay Dependent ◽  
Varying Delay

This paper deals with the master-slave synchronization problem of Lur'e systems based on time-varying delay feedback control. The time-varying delay is only assumed to be bounded. Delay-dependent conditions are derived such that the controlled slave system can track the master system. The synchronization criteria are expressed in terms of linear matrix inequality, which can be checked readily by using some standard numerical packages. A simulation example is provided to demonstrate the effectiveness of the proposed approach.

New Criterion for Stability of Linear Systems with Interval Time-Varying Delay

2014 ◽  
Vol 651-653 ◽  
pp. 2339-2342
Author(s):  
Ting Ting Wang ◽  
Zhao Di Xu ◽  
Hong Su
Keyword(s):  
Linear Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
New Criterion ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper is concerned with the delay-dependent stability for linear systems. Through constructing a new augmented LKF and using a new integral inequality, the improved delay-dependent stability criteria are derived in terms of linear matrix inequalities, and it is established that the results have less conservativ`e than some existing stability conditions. Finally, numerical examples are given to illustrate the effectiveness of the proposed result.

Sign in / Sign up

Export Citation Format

Share Document