scholarly journals New Stability Analysis Results for Linear System with Two Additive Time-Varying Delay Components

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Haitao Liu ◽  
Fang Liu
Keyword(s):  
Computational Complexity ◽  
Estimation Error ◽  
Time Varying ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Adequate Information ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper focuses on the stability problems of continuous linear systems with two additive time-varying delay components. Firstly, an effective and simple Lyapunov–Krasovskii functional (LKF) is established, which not only takes adequate information of delay components and their upper bounds into consideration but also establishes a simpler form to decrease the computational complexity. Secondly, an improved delay-dependent stability criterion together with its corollary is obtained by employing the generalized free-weighting-matrix-based (GFWM-based) inequality and some other techniques to calculate the derivative of the constructed LKF, which will further reduce the introduced estimation error and make the criteria less conservative. Lastly, a numerical example is presented to illustrate the less conservatism and lower computational complexity of the derived results.

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.

New Delay-Dependent Robust Stability Criterion for Uncertain Stochastic Systems with Time-Varying Delays

2012 ◽  
Vol 461 ◽  
pp. 633-636
Author(s):  
Cheng Wang
Keyword(s):  
Robust Stability ◽  
Stability Criterion ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

The problem of delay-dependent robust stability of uncertain stochastic systems with time-varying delay is discussed in this paper. Based on the Lyapunov-Krasovskii theory and free-weighting matrix technique, new delay-dependent stability criterion is presented. The criterion is in terms of linear matrix inequality (LMI) which can be solved by various available algorithms.

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 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 A Delay Decomposition Approach to the Stability Analysis of Singular Systems with Interval Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Jianmin Jiao ◽  
Rui Zhang
Keyword(s):  
Singular Systems ◽  
Time Varying ◽  
Decomposition Approach ◽  
Interval Time ◽  
Time Varying Delay ◽  
Delay Decomposition Approach ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper investigates delay-dependent stability problem for singular systems with interval time-varying delay. An appropriate Lyapunov-Krasovskii functional is constructed by decomposing the delay interval into multiple equidistant subintervals, where both the information of every subinterval and time-varying delay have been taken into account. Employing the Lyapunov-Krasovskii functional, improved delay-dependent stability criteria for the considered systems to be regular, impulse-free, and stable are established. Finally, two numerical examples are presented to show the effectiveness and less conservativeness of the proposed method.

New Delay-Dependent Approach on Stability for Systems with Interval Time-Varying Delay

2011 ◽  
Vol 181-182 ◽  
pp. 325-329
Author(s):  
Tao Zhang ◽  
Yan Qiu Cui ◽  
Juan Wang ◽  
Jin Sheng Sun
Keyword(s):  
Model Transformation ◽  
Time Varying ◽  
Stability Criteria ◽  
Theoretical Derivation ◽  
Interval Time ◽  
Time Varying Delay ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

In this paper, the stability of systems with interval time-varying delay is investigated. The time delay varies in an interval. By employing a new and tighter integral inequality and constructing an appropriate type of Lyapunov functional, the delay-dependent stability criteria are derived. Because neither any model transformation nor free weighting matrices are employed in the theoretical derivation, the developed stability criteria significantly improve and simplify the existing stability conditions.

New Criteria on Delay-Dependent Stability for Lurie Type System with Time-Varying Delay

2013 ◽  
Vol 846-847 ◽  
pp. 405-408
Author(s):  
He Li ◽  
Zhao Di Xu ◽  
Xian Tao Meng
Keyword(s):  
Type System ◽  
Type Systems ◽  
Time Varying ◽  
Time Varying Delay ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Partitioning ◽  
Delay Dependent Stability ◽  
Varying Delay ◽  
New Criteria

This paper study the problem of the stability analysis for Lurie type systems with time-varying delay. By exploiting a suitable Lyapunov-Krasovskii functional, new criteria on delay-dependent stability are derived. Some better results are obtained by using a delay partitioning approach and reciprocally convex technique. Finally, numerical examples are presented to illustrate the effectiveness and reduced conservatism of the obtain results.

scholarly journals Convex Polyhedron Method to Stability of Continuous Systems with Two Additive Time-Varying Delay Components

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Tiejun Li ◽  
Junkang Tian
Keyword(s):  
Stability Criterion ◽  
Convex Polyhedron ◽  
Linear Matrix ◽  
Continuous Systems ◽  
Time Varying ◽  
Time Varying Delay ◽  
Polyhedron Method ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper is concerned with delay-dependent stability for continuous systems with two additive time-varying delay components. By constructing a new class of Lyapunov functional and using a new convex polyhedron method, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities. The obtained stability criterion is less conservative than some existing ones. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

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