Abstract
In the last two decades, there has been much study of continuous-time nonlinear systems, but there are only a few results of the adaptive control problem of discrete-time nonlinear systems；where some simple nonlinear systems are studied，but the stability and asymptotic optimality of the resulting closed-loop systems cannot be directly extended to general nonlinear stochastic systems. It is well known that the bilinear systems is a kind of simple nonlinear systems．Many practical system models are bilinear， and the realization of more complex or more general nonlinear systems in work point can be attained by bilinear models. In this way we can obtain the approximate models of the nonlinear systems which are difficult to be
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