scholarly journals Stability Analysis of Systems with Interval Time-Varying Delays via a New Integral Inequality

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Zerong Ren ◽  
Jun-kang Tian
Keyword(s):  
Stability Analysis ◽  
Integral Inequality ◽  
Convex Combination ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Interval Time ◽  
Reciprocally Convex Combination ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper focuses on delay-dependent stability analysis for systems with interval time-varying delays. Based on a new integral inequality and a generalized reciprocally convex combination matrix inequality, a new delay-dependent stability criterion is obtained in terms of a linear matrix inequality (LMI). Finally, the merits of the proposed criterion are shown by two numerical examples.

scholarly journals Novel Delay-Dependent Stability Criteria for Discrete-Time Neural Networks with Time-Varying Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Sreten Stojanovic ◽  
Milan Stojanovic ◽  
Milos Stevanovic
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Convex Combination ◽  
Linear Matrix ◽  
Time Varying ◽  
Stability Criteria ◽  
Time Varying Delay ◽  
Reciprocally Convex Combination ◽  
Delay Dependent ◽  
Delay Dependent Stability

The delay-dependent stability problem is investigated for discrete-time neural networks with time-varying delays. A new augmented Lyapunov-Krasovskii functional (LKF) with single and double summation terms and several augmented vectors is proposed by decomposing the time-delay interval into two nonequidistant subintervals to derive less conservative stability conditions. Then, by using Wirtinger-based inequality, reciprocally, and extended reciprocally convex combination lemmas, tight estimations for sum terms in the forward difference of the LKF are given. Several zero equalities are introduced to further relax the existing results. Less conservative stability criteria are proposed in terms of linear matrix inequalities (LMIs). Finally, numerical examples are proposed to show the effectiveness and less conservativeness of the proposed method.

Delay-Dependent Stability Criteria for Systems with Distributed and Interval Time-Varying Delays

2012 ◽  
Vol 263-266 ◽  
pp. 1265-1268
Author(s):  
Cheng Wang ◽  
Qing Zhang ◽  
Jian Ping Gan
Keyword(s):  
Stability Problem ◽  
Model Transformation ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
Interval Time ◽  
Key Features ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper deals with the robust stability problem of distributed systems with interval time-varying delays. The key features of the approach include the introduction of suitable Lyapunov-Krasovskii functional and use of tighter bounding technology. A delay-dependent stability criterion is derived by using linear matrix inequality (LMI) techniques without using either free weighting matrices or model transformation. The criterion can be efficiently solved with available computational software.

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.

On Improved Delay-Range-Dependent Stability Criteria for Linear Systems with Interval Time-Varying Delay

2013 ◽  
Vol 427-429 ◽  
pp. 1306-1310
Author(s):  
Jun Jun Hui ◽  
He Xin Zhang ◽  
Fei Meng ◽  
Xin Zhou
Keyword(s):  
Functional Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Stability Criteria ◽  
Interval Time ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

In this paper, we consider the problem of robust delay-dependent stability for a class of linear uncertain systems with interval time-varying delay. By using the directly Lyapunov-Krasovskii (L-K) functional method, integral inequality approach and the free weighting matrix technique, new less conservative stability criteria for the system is formulated in terms of linear matrix inequalities .Numerical examples are given to show the effectiveness of the proposed approach.

scholarly journals Stability Analysis for Delayed Neural Networks: Reciprocally Convex Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Hongjun Yu ◽  
Xiaozhan Yang ◽  
Chunfeng Wu ◽  
Qingshuang Zeng
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Convex Combination ◽  
Linear Matrix ◽  
Delayed Neural Networks ◽  
Time Varying Delay ◽  
Reciprocally Convex Combination ◽  
Combination Approach ◽  
Continuous Neural Networks ◽  
Delay Dependent

This paper is concerned with global stability analysis for a class of continuous neural networks with time-varying delay. The lower and upper bounds of the delay and the upper bound of its first derivative are assumed to be known. By introducing a novel Lyapunov-Krasovskii functional, some delay-dependent stability criteria are derived in terms of linear matrix inequality, which guarantee the considered neural networks to be globally stable. When estimating the derivative of the LKF, instead of applying Jensen’s inequality directly, a substep is taken, and a slack variable is introduced by reciprocally convex combination approach, and as a result, conservatism reduction is proved to be more obvious than the available literature. Numerical examples are given to demonstrate the effectiveness and merits of the proposed method.

scholarly journals Improved Delay-Dependent Stability Analysis for Neural Networks with Interval Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Jun-kang Tian ◽  
Yan-min Liu
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Upper And Lower Bounds ◽  
Linear Matrix ◽  
Time Varying ◽  
Interval Time ◽  
Time Varying Delay ◽  
Improved Stability ◽  
Delay Dependent ◽  
Delay Partitioning

The problem of delay-dependent asymptotic stability analysis for neural networks with interval time-varying delays is considered based on the delay-partitioning method. Some less conservative stability criteria are established in terms of linear matrix inequalities (LMIs) by constructing a new Lyapunov-Krasovskii functional (LKF) in each subinterval and combining with reciprocally convex approach. Moreover, our criteria depend on both the upper and lower bounds on time-varying delay and its derivative, which is different from some existing ones. Finally, a numerical example is given to show the improved stability region of the proposed results.

scholarly journals LMI-Based Results on Robust Exponential Passivity of Uncertain Neutral-Type Neural Networks with Mixed Interval Time-Varying Delays via the Reciprocally Convex Combination Technique

Computation ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 70
Author(s):  
Nayika Samorn ◽  
Narongsak Yotha ◽  
Pantiwa Srisilp ◽  
Kanit Mukdasai
Keyword(s):  
Neural Networks ◽  
Model Transformation ◽  
Convex Combination ◽  
Neutral Type ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Interval Time ◽  
Combination Technique ◽  
Reciprocally Convex Combination

The issue of the robust exponential passivity analysis for uncertain neutral-type neural networks with mixed interval time-varying delays is discussed in this work. For our purpose, the lower bounds of the delays are allowed to be either positive or zero adopting the combination of the model transformation, various inequalities, the reciprocally convex combination, and suitable Lyapunov–Krasovskii functional. A new robust exponential passivity criterion is received and formulated in the form of linear matrix inequalities (LMIs). Moreover, a new exponential passivity criterion is also examined for systems without uncertainty. Four numerical examples indicate our potential results exceed the previous results.

scholarly journals Stability analysis of uncertain stochastic systems with interval time-varying delays and nonlinear uncertainties via augmented Lyapunov functional

Filomat ◽  
2012 ◽  
Vol 26 (6) ◽  
pp. 1179-1188
Author(s):  
R. Jeetendra ◽  
Vernold Vivin
Keyword(s):  
Lyapunov Functional ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Lower And Upper Bounds ◽  
Parameter Uncertainties ◽  
Interval Time ◽  
Nonlinear Uncertainties ◽  
Delay Dependent ◽  
Delay Dependent Stability

In this work, the problem of delay-dependent stability for uncertain stochastic systems with interval time-varying delays and nonlinear uncertainties is addressed. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. By constructing an augmented Lyapunov functional, a new delay interval-dependent stability criterion for the system is obtained in terms of Linear Matrix Inequalities (LMIs). Comparisons are made through numerical examples and less conservatism results are reported.

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