New Stability Analysis for Systems with Interval Time-varying Delay Based on Lyapunov Functional Method

2014 ◽  
Vol 11 (6) ◽  
pp. 1843-1851 ◽  
Author(s):  
Juan Liu
Keyword(s):  
Stability Analysis ◽  
Lyapunov Functional ◽  
Functional Method ◽  
Time Varying ◽  
Interval Time ◽  
Time Varying Delay ◽  
Lyapunov Functional Method ◽  
Varying Delay

scholarly journals A Novel Stability Analysis of Uncertain Switched Systems with Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Ganji Huang ◽  
Shixian Luo ◽  
Linna Wei ◽  
Wuhua Chen
Keyword(s):  
Switched Systems ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Time Varying ◽  
System Parameters ◽  
Time Varying Delay ◽  
Lyapunov Functional Method ◽  
The Stability ◽  
Varying Delay

This paper deals with the stability of switched systems with time-varying delay. The time-varying system parameters are assumed to be norm-bounded. Based on a novel switched time-varying Lyapunov functional method, some new LMI-based sufficient conditions have been obtained to ensure the exponential stability for the uncertain switched delays systems. Finally, the proposed method is applied to a numerical example and the simulative results are also given.

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 Novel Robust Stability Criteria of Uncertain Systems with Interval Time-Varying Delay Based on Time-Delay Segmentation Method and Multiple Integrals Functional

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Xing He ◽  
Li-Jun Song ◽  
Yu-Bin Wu ◽  
Zi-Yu Zhou
Keyword(s):  
Stability Analysis ◽  
Robust Stability ◽  
Stability Criterion ◽  
Uncertain Systems ◽  
Previous Literature ◽  
Time Varying ◽  
Interval Time ◽  
Time Varying Delay ◽  
Varying Delay ◽  
Better Than

Interval time-varying delay is common in control process, e.g., automatic robot control system, and its stability analysis is of great significance to ensure the reliable control of industrial processes. In order to improve the conservation of the existing robust stability analysis method, this paper considers a class of linear systems with norm-bounded uncertainty and interval time-varying delay as the research object. Less conservative robust stability criterion is put forward based on augmented Lyapunov-Krasovskii (L-K) functional method and reciprocally convex combination. Firstly, the delay interval is partitioned into multiple equidistant subintervals, and a new Lyapunov-Krasovskii functional comprising quadruple-integral term is introduced for each subinterval. Secondly, a novel delay-dependent stability criterion in terms of linear matrix inequalities (LMIs) is given by less conservative Wirtinger-based integral inequality approach. Three numerical comparative examples are given to verify the superiority of the proposed approach in reducing the conservation of conclusion. For the first example about closed-loop control systems with interval time-varying delays, the proposed robust stability criterion could get MADB (Maximum Allowable Delay Bound) about 0.3 more than the best results in the previous literature; and, for two other uncertain systems with interval time-varying delays, the MADB results obtained by the proposed method are better than those in the previous literature by about 0.045 and 0.054, respectively. All the example results obtained in this paper clearly show that our approach is better than other existing methods.

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