In this paper, adaptive control of a class of nonlinear discrete time dynamical systems with boundedness of all signals is established by using a linear robust adaptive controller and a neural network based nonlinear adaptive controller, acid switching between them by a suitably defined switching law. The linear controller, when used alone, assures boundedness of all the signals but not satisfactory performance. The nonlinear controller may result in improved response. but may also result in instability. By using a switching scheme, it is demonstrated that improved performance and stability can be simultaneously achieved.