On uniform ultimate boundedness of linear systems with time-varying delays and peak-bounded disturbances

Yucai Ding, Hui Liu, Hui Xu and Shouming Zhong

Applied Mathematics and Computation, 2019, vol. 349, issue C, 381-392

Abstract: This paper is devoted to a problem of uniform ultimate boundedness (UUB) for a class of linear systems with interval time-varying delays and peak-bounded disturbances. By using the Lyapunov–Krasovskii functional method, a general UUB condition and an estimation of the ultimate bound on system trajectories are developed. On the basis of the above results, linear matrix inequality (LMI) conditions on UUB of the perturbed systems under consideration are derived by constructing an appropriate Lyapunov–Krasovskii functional. Meanwhile, the ultimate bound for a prescribed disturbance attenuation level is given in the form of an ellipsoidal surface. The feasibility and effectiveness of the derived results are illustrated by two numerical examples.

Keywords: Uniform ultimate boundedness; Ultimate bound; Peak-bounded disturbance; Time-varying delay; Linear matrix inequality (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:349:y:2019:i:c:p:381-392

DOI: 10.1016/j.amc.2018.12.068

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