On reachable set estimation of two‐dimensional systems described by the Roesser model with time‐varying delays

Summary In this paper, the problem of reachable set estimation of two‐dimensional (2‐D) discrete‐time systems described by the Roesser model with interval time‐varying delays is considered for the first time. New 2‐D weighted summation inequalities, which provide a tighter lower bound than the commo...

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Bibliographic Details
Published in:International journal of robust and nonlinear control 2018-01, Vol.28 (1), p.227-246
Main Authors: Trinh, Hieu, Hien, Le Van
Format: Article
Language:English
Subjects:
2‐D systems
Computer programs
Discrete time systems
Linear matrix inequalities
Lower bounds
Mathematical analysis
Mathematical models
Matrix methods
reachable set estimation
Roesser model
Stability analysis
System effectiveness
time‐varying delays
Two dimensional analysis
Two dimensional models
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Summary:Summary In this paper, the problem of reachable set estimation of two‐dimensional (2‐D) discrete‐time systems described by the Roesser model with interval time‐varying delays is considered for the first time. New 2‐D weighted summation inequalities, which provide a tighter lower bound than the commonly used Jensen summation inequality, are proposed. Based on the Lyapunov‐Krasovskii functional approach, and by using the 2‐D weighted summation inequalities presented in this paper, new delay‐dependent conditions are derived to ensure the existence of an ellipsoid that bounds the system states in the presence of bounded disturbances. The derived conditions are expressed in terms of linear matrix inequalities, which can be solved by various computational tools to determine a smallest possible ellipsoidal bound. Applications to exponential stability analysis of 2‐D systems with delays are also presented. The effectiveness of the obtained results are illustrated by numerical examples.
ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.3866