Reachable set estimation for linear systems with time-varying delay and polytopic uncertainties

2019 ◽  
Vol 356 (13) ◽  
pp. 7322-7346 ◽  
Author(s):  
Wenqin Wang ◽  
Shouming Zhong ◽  
Feng Liu ◽  
Jun Cheng
Keyword(s):  
Linear Systems ◽  
Reachable Set ◽  
Time Varying ◽  
Time Varying Delay ◽  
Set Estimation ◽  
Polytopic Uncertainties ◽  
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 Reachable Set Estimation for Uncertain Markovian Jump Systems with Time-Varying Delay and Disturbances

2021 ◽  
Vol 2021 ◽  
pp. 1-30
Author(s):  
Shouwei Zhou ◽  
Jiangliu Gu ◽  
Changchun Shen ◽  
Min Jiang
Keyword(s):  
Integral Inequality ◽  
Reachable Set ◽  
Time Varying ◽  
Markovian Jump ◽  
Time Varying Delay ◽  
Set Estimation ◽  
Reachable Set Estimation ◽  
Jump Systems ◽  
Uncertain Markovian Jump Systems ◽  
Varying Delay

In this paper, we are concerned with the problem of reachable set estimation for uncertain Markovian jump systems with time-varying delays and disturbances. The main consideration is to find a proper method to obtain the no-ellipsoidal bound of the reachable set of Markovian jump system as small as possible. Based on an augmented Lyapunov–Krasovskii functional, by dividing the time-varying delay into two nonuniform subintervals, more general delay-dependent stability criteria for the existence of a desired ellipsoid are derived. An optimized integral inequality which is based on distinguished Wirtinger integral inequality and reciprocally convex combination inequality is used to deal with the integral terms. Finally, numerical examples are presented to demonstrate the effectiveness of the theoretical results.

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