scholarly journals Stability Criteria of Interval Time-Varying Delay Systems and Their Application

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Zhanhui Lu ◽  
Chengyong Wang ◽  
Weijuan Wang
Keyword(s):  
Convex Combination ◽  
Combination Method ◽  
Delay Systems ◽  
Time Varying ◽  
Stability Criteria ◽  
Interval Time ◽  
Time Varying Delay ◽  
The Stability ◽  
Delay Dependent ◽  
Uncertain Linear Systems

The stability for a class of uncertain linear systems with interval time-varying delays is studied. Based on the delay-dividing approach, the delay interval is partitioned into two subintervals. By constructing an appropriate Lyapunov-Krasovskii functional and using the convex combination method and the improved integral inequality, the delay-dependent stability criteria with less conservation are derived. Finally, some numerical examples are given to show the effectiveness and superiority 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.

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

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
Boren Li
Keyword(s):  
Fast Time ◽  
Time Varying ◽  
Stability Criteria ◽  
Lower And Upper Bounds ◽  
Interval Time ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Uncertain Linear Systems ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper is concerned with robust stability of uncertain linear systems with interval time-varying delay. The time-varying delay is assumed to belong to an interval, which means that the derivative of the time-varying delay has an upper bound or a restriction. On other occasions, if we do not take restriction on the derivative of the time-varying delay into consideration, it allows the delay to be a fast time-varying function. The uncertainty under consideration includes a polytopic-type uncertainty and a linear fractional norm-bounded uncertainty. In order to obtain much less conservative results, a new Lyapunov-Krasovskii functional, which makes use of the information of both the lower and upper bounds of the interval time-varying delay, is proposed to derive some new stability criteria. Numerical examples are given to demonstrate the effectiveness of the proposed stability criteria.

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 Delay-Dependent Stability Conditions for Time-Varying Delay Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Wei Qian ◽  
Hamid Reza Karimi
Keyword(s):  
Delay Systems ◽  
Time Varying ◽  
Stability Criteria ◽  
Time Varying Delay ◽  
Decision Variables ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay ◽  
Theoretical Results ◽  
Reciprocally Convex Approach

This paper addresses the delay-dependent stability for systems with time-varying delay. First, by taking multi-integral terms into consideration, new Lyapunov-Krasovskii functional is defined. Second, in order to reduce the computational complexity of the main results, reciprocally convex approach and some special transformations are introduced, and new delay-dependent stability criteria are proposed, which are less conservative and have less decision variables than some previous results. Finally, two well-known examples are given to illustrate the correctness and advantage of our theoretical results.

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