Tracking control of nonlinear automobile idle-speed time-delay system via differential geometry approach

This paper is concerned with the problem of global asymptotical tracking of single-input single-output (SISO) nonlinear time-delay control systems. 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 a broad class of nonlinear time-delay control systems is developed. The underlying theoretical approaches are the differential geometry approach and the composite Lyapunov approach. One utilizes the parameterized co-ordinate transformation to transform the original nonlinear system into singularly perturbed model and the composite Lyapunov approach is then applied for output tracking. For the view of practical application, the proposed control methodology has been successfully applied to the famous nonlinear automobile idle-speed control system.