Observer-based control design for nonlinear systems with unknown delays

In this brief, we study the problem of designing observer-based controller for nonlinear system subject to unknown time-varying state delay. The unknown delay is assumed to be upper bounded, but nevertheless the bound is not required to be known. In order to tackle this interesting problem, we utilize a Halanay-inequality-based criterion which can guarantee exponential stability of the closed-loop system as well as the estimation error system. This exponential stability criterion allows us to design observer-based controller for the nonlinear time-delay system without invoking differentiability assumption on the unknown delay. A robotic system is considered to illustrate the efficiency of the new results.