Reachable set estimation and controller design for discrete‐time singularly perturbed systems with time‐varying delay

2021 ◽  
Author(s):  
Guobao Liu ◽  
Shengyuan Xu ◽  
Wenhui Liu ◽  
Yuming Chu ◽  
Zhengqiang Zhang
Keyword(s):  
Discrete Time ◽  
Controller Design ◽  
Singularly Perturbed ◽  
Time Varying ◽  
Singularly Perturbed Systems ◽  
Time Varying Delay ◽  
Set Estimation ◽  
Perturbed Systems ◽  
Reachable Set Estimation ◽  
Varying Delay

scholarly journals Reachable Set Estimation for Discrete-Time Systems with Interval Time-Varying Delays and Bounded Disturbances

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Jiemei Zhao ◽  
Yin Sheng
Keyword(s):  
Discrete Time ◽  
Reachable Set ◽  
Time Varying ◽  
Time Varying Delay ◽  
Set Estimation ◽  
Discrete Time Systems ◽  
Bounded Disturbances ◽  
Reachable Set Estimation ◽  
Time Systems ◽  
Varying Delay

The reachable set estimation problem for discrete-time systems with delay-range-dependent and bounded disturbances is investigated. A triple-summation term, the upper bound, and the lower bound of time-varying delay are introduced into the Lyapunov function. In this case, an improved delay-range-dependent criterion is established for the addressed problem by constructing the appropriate Lyapunov functional, which guarantees that the reachable set of discrete-time systems with time-varying delay and bounded peak inputs is contained in the ellipsoid. It is worth mentioning that the initial value of the system does not need to be zero. Then, the reachable set estimation problem for time-delay systems with polytopic uncertainties is investigated. The effectiveness and the reduced conservatism of the derived results are demonstrated by an illustrative example.

scholarly journals Stability Bound Analysis and Synthesis for Singularly Perturbed Systems with Time-Varying Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Fengqi Sun ◽  
Linna Zhou ◽  
Qingling Zhang ◽  
Yongxiang Shen
Keyword(s):  
Computational Cost ◽  
Singularly Perturbed ◽  
Time Varying ◽  
Singularly Perturbed Systems ◽  
Time Varying Delay ◽  
Stability Bound ◽  
Perturbed Systems ◽  
Analysis And Synthesis ◽  
Varying Delay ◽  
Bound Analysis

This paper addresses the problems of stability bound analysis and synthesis for singularly perturbed systems with time-varying delay. First, by constructing an appropriate Lyapunov-Krasovskii functional, a sufficient condition is derived for the system to be stable when the singular perturbation parameter is lower than a predefined upper bound which is referred to as the stability bound of the singularly perturbed system. The proposed criterion needs less computational cost than the existing ones. Then, a state feedback controller design method is proposed to achieve a prescribed stability bound, which can be applied to both standard and nonstandard singularly perturbed systems with time-varying delay. Finally, the effectiveness and merits of the proposed approach are shown through numerical examples.

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