I. Introduction
In recent decades, the analysis and design theories for singularly perturbed systems with time-delay have been of considerable concern. For example, Fridman[1] has considered the effect of small delay on stability of the singularly perturbed systems. In [2] and [3], the controllability problem of nonstandard singularly perturbed systems with small state delay and stabilization problem of nonstandard singularly perturbed systems with small delays both in state and control have been studied respectively. Also, for the optimal control problems for the singularly perturbed systems, many efficient optimal control methods for singularly perturbed systems are obtained. For instance, the nonlinear singularly perturbed optimal control via invariant manifolds [4] and a descriptor system approach [5] have been investigated, respectively. In [6] a composite control law for singularly perturbed bilinear systems via successive Galerkin approximation was presented. On the basis of singular decomposition theory and boundary layer models, Bouyekhf [7] gave a trajectory approximation results for particular class of singularly perturbed nonlinear discrete-time systems. These results are all for singularly perturbed systems without time-delay. However, for the optimal control of singularly perturbed systems with time-delay, there are few results are available [8].