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

We consider the problem of designing a feedback con- trol 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 Lya- punov method for nonlinear state feedback synthesis, a robust glob- ally 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 ap- proach. For the view of practical application, the proposed control methodology has been successfully applied to the famous nonlinear automobile idle-speed control system problem.