In this paper, a linear closed-loop Stackelberg strategy for a class of singularly perturbed stochastic systems (SPSS) governed by Itô differential equations is considered. Necessary conditions for the solution are established via a set of cross-coupled algebraic Lyapunov and Riccati equations (CAL-REs). After studying the asymptotic behavior of the solution for these stochastic equations, two new numerical algorithms based on Newton's method and semidefinite programming (SDP) for solving

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... are given. A numerical example is solved to demonstrate the efficiency of the proposed algorithm.