Open AccessNew results on state bounding for discrete‐time systems with interval time‐varying delay and bounded disturbance inputs
Author(s) -
Van Hien Le,
An Nguyen Thanh,
Trinh Hieu
Publication year - 2014
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2013.0980
Subject(s) - bounded function , bounding overwatch , control theory (sociology) , mathematics , interval (graph theory) , discrete time and continuous time , ellipsoid , exponential stability , regular polygon , convex combination , linear matrix inequality , mathematical optimization , convex optimization , computer science , mathematical analysis , nonlinear system , control (management) , physics , geometry , combinatorics , astronomy , artificial intelligence , quantum mechanics , statistics
This study considers the problem of state bounding for a class of discrete‐time systems with interval time‐varying delay and bounded disturbance inputs. By using an improved Lyapunov–Krasovskii functional combining with the delay‐decomposition technique and the reciprocally convex approach, the authors first derive new delay‐dependent conditions in terms of matrix inequalities to guarantee the existence of a ball such that, for any initial condition, the state trajectory of the system is either bounded within that ball or converges exponentially within it. On the basis of these new conditions, the authors then derive an improved ellipsoid reachable set bounding and a new result on exponential stability of discrete‐time systems with interval time‐varying delay. Numerical examples are presented to show the effectiveness of the obtained results and improvement over existing results.