Estimation of reachable set for interval time-varying delay systems

This paper deals with the problem of reachable set bounding for interval time-varying delay system with disturbances. A generalized reciprocally convex combination lemma and a new Lyapunov-Krasovskii functional (LKF) are given to obtain the delay-dependent criterion. The reachable set of time-varying delay systems with bounded peak disturbances is contained in the ellipsoid base this result. Meanwhile, the initial points are not required to be zero for the considered systems. Finally, a numerical example is given to demonstrate the effectiveness of the obtained results.