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

摘要

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.