Tracking and disturbance rejection in a nonlinear control system with time delay

We consider the problem of designing a feedback control law in order to reject the unknown bounded disturbance and achieve tracking of reference inputs in control systems described by a class of nonlinear time-delay differential-algebraic equations. Based on the input-output feedback linearization technique and Lyapunov method for nonlinear state feedback synthesis, a robust globally asymptotical output tracking controller design methodology for nonlinear time-delay control systems with delays on the states and the input is developed. The underlying theoretical approaches are the differential geometry approach and the composite Lyapunov approach. For the view of practical application, the proposed control methodology has been successfully applied to the famous nonlinear automobile idle-speed control system problem.