Abstract: The parametric adaptive control problem was studied for a class of affine nonlinear singular systems with unknown parameter.Firstly， the affine nonlinear singular systems were transformed into generally linear singular systems via diffeomorphic transformation using Lie derivative and Lie bracket.Then， combined with LMI method and the Lyapunov stability theory， the parametric adaptive control method was used to construct an adaptive regulator.What’s more， a sufficient condition was given under which the system was asymptotically stable at the point of equilibrium and parameter error was asymptotically convergent.Lastly， a simulation was constructed using Matlab， and the results of simulation showed the effectiveness and feasibility of the presented method.

Key words: affine nonlinear singular system, parametric adaptive control, diffeomorphic transformation, LMI method, Lyapunov stability theory