Improved stability conditions of time-varying delay systems based on new Lyapunov functionals

2018 ◽  
Vol 355 (3) ◽  
pp. 1176-1191 ◽  
Author(s):  
Tae H. Lee ◽  
Ju H. Park
Keyword(s):  
Delay Systems ◽  
Stability Conditions ◽  
Lyapunov Functionals ◽  
Time Varying ◽  
Time Varying Delay ◽  
Improved Stability ◽  
Varying Delay

scholarly journals New Stability Conditions for a Class of Nonlinear Discrete-Time Systems with Time-Varying Delay

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1531 ◽  
Author(s):  
Sami Elmadssia ◽  
Karim Saadaoui
Keyword(s):  
Discrete Time ◽  
Delay Systems ◽  
Stability Conditions ◽  
Time Varying ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Aggregation Techniques ◽  
Discrete Time Delay ◽  
Time Systems ◽  
Varying Delay

In this paper, the stability problem of discrete time delay systems is investigated. The class of systems under consideration is represented by delayed difference equations and models nonlinear discrete time systems with time varying delay. It is transformed into an arrow from matrix representation which allows the use of aggregation techniques and M-matrix properties to determine novel sufficient stability conditions. The originalities of our findings are shown in their explicit representation, using system’s parameters, as well as in their easiness to be employed. The obtained results demonstrate also that checking stability of nonlinear discrete time systems with time varying delay can be reduced to an M-matrix test. Next, it is shown how to use our method in designing a state feedback controller that stabilizes a discrete time Lure system with time varying delay and sector bounded nonlinearity. Finally, several examples are provided to show the effectiveness of the introduced technique.

scholarly journals An improved stability criterion for linear time-varying delay systems

Automatika ◽  
2019 ◽  
Vol 61 (2) ◽  
pp. 229-237
Author(s):  
Wenxi Feng ◽  
Fei Luo ◽  
Wenyong Duan ◽  
Yan Li ◽  
Jian Chen
Keyword(s):  
Stability Criterion ◽  
Linear Time ◽  
Delay Systems ◽  
Time Varying ◽  
Time Varying Delay ◽  
Improved Stability ◽  
Varying Delay

Conservativeness Judgement of Controller for Systems with Time-Varying Delay

2012 ◽  
Vol 249-250 ◽  
pp. 1173-1179
Author(s):  
Jiu Ying Deng ◽  
Hui Fei Deng ◽  
Jian Bin Xiong ◽  
Qin Ruo Wang
Keyword(s):  
Delay System ◽  
Delay Systems ◽  
Descriptor System ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Optimization Approach ◽  
Time Varying ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Varying Delay

The conservatism of asymptotic stability conditions is considered in terms of linear matrix inequalities for time-varying delay systems. The conservative index is defined to evaluate the conservativeness for both delay-dependent and delay-independent stability conditions. The general results on performance analysis are presented based on descriptor system approach. The conservativeness index is defined for time-varying delay system. The optimization approach is given to obtain the upper delay and rational performances for the state-feedback controller of time-delay systems. Experimental results verify the effectiveness of the new method.

scholarly journals Improved Stability Method for Linear Time-Varying Delay Systems

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 7753-7758 ◽  
Author(s):  
Zhanshan Zhao ◽  
Meili He ◽  
Jing Zhang ◽  
Jie Sun
Keyword(s):  
Linear Time ◽  
Delay Systems ◽  
Time Varying ◽  
Time Varying Delay ◽  
Improved Stability ◽  
Stability Method ◽  
Varying Delay
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