On local ISS of nonlinear second‐order time‐delay systems without damping

Abstract

SummaryFor a second‐order system with vector position, either constant or time‐varying delays, and a power nonlinearity of the degree higher than one, which does not contain a velocity‐proportional damping term, the conditions of local input‐to‐state stability are proposed. The result is based on application of Lyapunov‐Razumikhin approach, for which new time estimates on decay of solutions are obtained. The approach is extended to attitude stabilization of a rigid body, and it is illustrated by simulations.