An ellipsoid bounding of reachable systems with delay and bounded peak inputs

Abstract

Linear systems with constant coefficients and time-varying delays are considered. We address the problem of finding an ellipsoid that bounds the set of the states (in the Euclidean space) that are reachable from the origin in finite time by inputs with peak value that is bounded by a prechosen positive scalar. The system may encounter uncertainties in the matrices of its state space model and in the delay length. The Lyapunov-Razumikhin approach is applied and a bounding ellipsoid is obtained by solving a set of linear matrix inequalities that depend on the upper-bound of the delay length.