Novel stability criteria for linear time-delay systems using Lyapunov-Krasovskii functionals with a cubic polynomial on time-varying delay

2020 ◽  
pp. 1-9 ◽  
Author(s):  
Xian-Ming Zhang ◽  
Qing-Long Han ◽  
Xiaohua Ge
Keyword(s):  
Time Delay ◽  
Linear Time ◽  
Delay Systems ◽  
Time Varying ◽  
Time Delay Systems ◽  
Stability Criteria ◽  
Time Varying Delay ◽  
Cubic Polynomial ◽  
Varying Delay

scholarly journals Robustl2-l∞Filtering for Discrete-Time Delay Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Chengming Yang ◽  
Zhandong Yu ◽  
Pinchao Wang ◽  
Zhen Yu ◽  
Hamid Reza Karimi ◽  
...  
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Estimation Error ◽  
Delay Systems ◽  
Time Varying ◽  
Time Delay Systems ◽  
Time Varying Delay ◽  
Discrete Time Delay ◽  
Error System ◽  
Varying Delay

The problem of robustl2-l∞filtering for discrete-time system with interval time-varying delay and uncertainty is investigated, where the time delay and uncertainty considered are varying in a given interval and norm-bounded, respectively. The filtering problem based on thel2-l∞performance is to design a filter such that the filtering error system is asymptotically stable with minimizing the peak value of the estimation error for all possible bounded energy disturbances. Firstly, sufficientl2-l∞performance analysis condition is established in terms of linear matrix inequalities (LMIs) for discrete-time delay systems by utilizing reciprocally convex approach. Then a less conservative result is obtained by introducing some variables to decouple the Lyapunov matrices and the filtering error system matrices. Moreover, the robustl2-l∞filter is designed for systems with time-varying delay and uncertainty. Finally, a numerical example is given to demonstrate the effectiveness of the filter design method.

scholarly journals Further Stability Analysis of Time-Delay Systems with Nonlinear Perturbations

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Jie Sun ◽  
Jing Zhang
Keyword(s):  
Stability Analysis ◽  
Delay Systems ◽  
Time Varying ◽  
Time Delay Systems ◽  
Nonlinear Perturbations ◽  
Stability Criteria ◽  
Double Integral ◽  
Time Varying Delay ◽  
Integral Forms ◽  
Varying Delay

In this study, we focus on stability analysis for systems with time-varying delay and nonlinear perturbations. In order to cut down the conservatism of the existing stability criteria, we utilize the triple integral forms of Lyapunov-Krasovskii functional (LKF). In addition, by using single and double integral forms of Wirtinger-based inequality, we overcome some conservatism which come from Jensen’s inequality. Three well-known numerical examples are given at the end. Compared with some existing results, our results have less conservatism.

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