Reachable Set Estimation of Switched Genetic Regulatory Networks with Mixed Delays and Bounded Disturbances*

2020 ◽  
Author(s):  
Xian Zhang ◽  
Lina Zhang ◽  
Yu Xue ◽  
Xin Wang ◽  
Mouquan Shen ◽  
...  
Keyword(s):  
Regulatory Networks ◽  
Genetic Regulatory Networks ◽  
Reachable Set ◽  
Mixed Delays ◽  
Set Estimation ◽  
Bounded Disturbances ◽  
Reachable Set Estimation

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 New Results on Reachable Set Estimation and Controller Design for Linear Systems with Mixed Delays via Triple Integral Functionals

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Wei Kang ◽  
Shouming Zhong
Keyword(s):  
Linear Systems ◽  
State Feedback ◽  
Controller Design ◽  
Reachable Set ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Closed Loop System ◽  
Set Estimation ◽  
Reachable Set Estimation ◽  
Bounded Disturbance

This paper is concerned with the problem of reachable set estimation and controller design for a class of linear systems with mixed delays and bounded disturbance inputs. By constructing a newly augmented Lyapunov-Krasovskii functional, combining with triple integral technique and reciprocally convex approach, some new reachable set estimation conditions are derived in terms of linear matrix inequalities. Based on these conditions, a state-feedback controller has been designed to ensure the reachable set of the closed-loop system bounded by a given ellipsoid. Finally, two numerical examples are given to illustrate the effectiveness of the proposed analysis and designed method.

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