Delay partitioning approach to robust stability analysis for uncertain stochastic systems with interval time-varying delay

2012 ◽  
Vol 6 (7) ◽  
pp. 875 ◽  
Author(s):  
C. Wang ◽  
Y. Shen
Keyword(s):  
Stability Analysis ◽  
Robust Stability ◽  
Stochastic Systems ◽  
Time Varying ◽  
Interval Time ◽  
Time Varying Delay ◽  
Robust Stability Analysis ◽  
Delay Partitioning ◽  
Varying Delay

On robust stability for uncertain neutral systems with non-differentiable interval time-varying discrete delay and nonlinear perturbations

2017 ◽  
Vol 11 (01) ◽  
pp. 1850007 ◽  
Author(s):  
Peerapongpat Singkibud ◽  
Kanit Mukdasai
Keyword(s):  
Robust Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Neutral Systems ◽  
Interval Time ◽  
Time Varying Delay ◽  
Robust Stability Analysis ◽  
Discrete Interval ◽  
Varying Delay

In this paper, we investigate the problem of delay-range-dependent robust stability analysis for uncertain neutral systems with interval time-varying delays and nonlinear perturbations. The restriction on the derivative of the discrete interval time-varying delay is removed. By applying the augmented Lyapunov–Krasovskii functional approach, new improved integral inequalities, descriptor model transformation, Leibniz–Newton formula and utilization of zero equation, new delay-range-dependent robust stability criteria are derived in terms of linear matrix inequalities (LMIs) for the considered systems. Numerical examples have shown to illustrate the significant improvement on the conservatism of the delay upper bound over some reported results.

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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