Linear Matrix Inequality Approach to New Delay-Dependent Stability Criteria for Uncertain Dynamic Systems with Time-Varying Delays

2011 ◽  
Vol 149 (3) ◽  
pp. 630-646 ◽  
Author(s):  
O. M. Kwon ◽  
S. M. Lee ◽  
Ju H. Park
Keyword(s):  
Linear Matrix Inequality ◽  
Dynamic Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
Uncertain Dynamic Systems ◽  
Linear Matrix Inequality Approach ◽  
Delay Dependent ◽  
Delay Dependent Stability

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 Global Dissipativity on Uncertain Discrete-Time Neural Networks with Time-Varying Delays

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Qiankun Song ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Computationally Efficient ◽  
Inequality Technique ◽  
General Activation ◽  
Delay Dependent

The problems on global dissipativity and global exponential dissipativity are investigated for uncertain discrete-time neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing linear matrix inequality technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Illustrated examples are given to show the effectiveness of the proposed criteria. It is noteworthy that because neither model transformation nor free-weighting matrices are employed to deal with cross terms in the derivation of the dissipativity criteria, the obtained results are less conservative and more computationally efficient.

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 Delay-Dependent Stability Analysis for Recurrent Neural Networks with Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Shu Lv ◽  
Junkang Tian ◽  
Shouming Zhong
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Activation Functions ◽  
New Class ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper concerns the problem of delay-dependent stability criteria for recurrent neural networks with time varying delays. By taking more information of states and activation functions as augmented vectors, a new class of the Lyapunov functional is proposed. Then, some less conservative stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.

scholarly journals Stability Criteria for Singular Stochastic Hybrid Systems with Mode-Dependent Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Ming Zhao ◽  
Yueying Wang ◽  
Pingfang Zhou ◽  
Dengping Duan
Keyword(s):  
Hybrid Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
Stochastic Hybrid Systems ◽  
Time Varying Delay ◽  
Exponentially Stable ◽  
Delay Dependent ◽  
Varying Delay

This paper provides a delay-dependent criterion for a class of singular stochastic hybrid systems with mode-dependent time-varying delay. In order to reduce conservatism, a new Lyapunov-Krasovskii functional is constructed by decomposing the delay interval into multiple subintervals. Based on the new functional, a stability criterion is derived in terms of strict linear matrix inequality (LMI), which guarantees that the considered system is regular, impulse-free, and mean-square exponentially stable. Numerical examples are presented to illustrate the effectiveness of proposed method.

Novel Approach to Robust Stability Criteria of Uncertain System with Time-Varying Delay

2013 ◽  
Vol 631-632 ◽  
pp. 1189-1194
Author(s):  
Chao Deng ◽  
Zhao Di Xu ◽  
Yu Bai ◽  
Xin Yuan Wang
Keyword(s):  
Linear Matrix Inequality ◽  
Robust Stability ◽  
Uncertain System ◽  
Linear Matrix ◽  
Convexity Property ◽  
Time Varying ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
Time Varying Delay ◽  
Varying Delay

This paper considers the robust stability criteria of uncertain system with time-varying delay. Firstly, by exploiting a new Lyapunov function that optimizes the segment of time delay and using the convexity property and free-weight method of the Linear Matrix Inequality, delay-dependent stability condition can be obtained for the asymptotical stability of the nominal system. Secondly, basing on the obtained condition, the corresponding linear matrix inequality can be obtained for the uncertain system. Finally, an example is given to demostrate the effectiveness and the merit of the proposed method.

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