Abstract: The design of adaptive control for a class of nonlinear singular switched systems satisfying the Lipschitz condition was studied. First， the design of the basic adaptive control of a single input nonlinear singular switching system was studied. The controller was designed to stabilize the system. Then， the adaptive gain and the gain adjustment based on the Lyapunov stability theorem presented by the single input nonlinear singular switching system were used to expand the tracking problem of multi-input singular switching systems and an adaptive control method was designed. Finally， a numerical simulation was performed using Matlab to illustrate the effectiveness of the proposed control method. The proposed controller has a very simple structure and is easy to be applied in practice.

Key words: Lipschitz condition, adaptive control, nonlinear switched singular system, stability, tracking error