scholarly journals LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties

2012 ◽  
Vol 22 (2) ◽  
pp. 339-351 ◽  
Author(s):  
Pagavathigounder Balasubramaniam ◽  
Shanmugam Lakshmanan ◽  
Rajan Rakkiyappan
Keyword(s):  
Robust Stability ◽  
Optimization Problem ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Stability Criteria ◽  
Lmi Optimization ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Delay Dependent Stability

LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertaintiesThis paper studies an LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties. The delay is assumed to be time-varying and belong to a given interval, which means that lower and upper bounds of this interval time-varying delay are available. The uncertainty under consideration includes polytopic-type uncertainty and linear fractional norm-bounded uncertainty. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, delay-dependent stability criteria are obtained in terms of Linear Matrix Inequalities (LMIs). Moreover, the derivative of time delays is allowed to take any value. Finally, four numerical examples are given to illustrate the effectiveness of the proposed method and to show an improvement over some results found in the literature.

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 Robust Stability Criteria for Uncertain Neutral Systems with Interval Nondifferentiable Time-Varying Delay and Nonlinear Perturbations

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
W. Weera ◽  
P. Niamsup
Keyword(s):  
Robust Stability ◽  
Linear Matrix ◽  
Fast Time ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Stability Criteria ◽  
Neutral Systems ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Varying Delay

We study the robust stability criteria for uncertain neutral systems with interval time-varying delays and time-varying nonlinear perturbations simultaneously. The constraint on the derivative of the time-varying delay is not required, which allows the time-delay to be a fast time-varying function. Based on the Lyapunov-Krasovskii theory, we derive new delay-dependent stability conditions in terms of linear matrix inequalities (LMIs) which can be solved by various available algorithms. Numerical examples are given to demonstrate that the derived conditions are much less conservative than those given in the literature.

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 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.

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.

scholarly journals Delay-Dependent Stability Criteria for Singular Systems with Interval Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Jianmin Jiao
Keyword(s):  
Singular Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Stability Criteria ◽  
Interval Time ◽  
Time Varying Delay ◽  
Decision Variables ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper is concerned with stability analysis for singular systems with interval time-varying delay. By constructing a novel Lyapunov functional combined with reciprocally convex approach and linear matrix inequality (LMI) technique, improved delay-dependent stability criteria for the considered systems to be regular, impulse free, and stable are established. The developed results have advantages over some previous ones as they involve fewer decision variables yet less conservatism. Numerical examples are provided to demonstrate the effectiveness of the proposed stability results.

scholarly journals Improved Delay-Dependent Robust Stability Criteria for a Class of Uncertain Neutral Type Lur’e Systems with Discrete and Distributed Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Kaibo Shi ◽  
Hong Zhu ◽  
Shouming Zhong ◽  
Yong Zeng ◽  
Yuping Zhang
Keyword(s):  
Robust Stability ◽  
Neutral Type ◽  
Distributed Delays ◽  
Linear Matrix ◽  
Time Varying ◽  
Stability Criteria ◽  
Lur’E Systems ◽  
Robust Stability Analysis ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper is concerned with the problem of delay-dependent robust stability analysis for a class of uncertain neutral type Lur’e systems with mixed time-varying delays. The system has not only time-varying uncertainties and sector-bounded nonlinearity, but also discrete and distributed delays, which has never been discussed in the previous literature. Firstly, by employing one effective mathematical technique, some less conservative delay-dependent stability results are established without employing the bounding technique and the mode transformation approach. Secondly, by constructing an appropriate new type of Lyapunov-Krasovskii functional with triple terms, improved delay-dependent stability criteria in terms of linear matrix inequalities (LMIs) derived in this paper are much brief and valid. Furthermore, both nonlinearities located in finite sector and infinite one have been also fully taken into account. Finally, three numerical examples are presented to illustrate lesser conservatism and the advantage of the proposed main results.

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