<p>In this paper, the asynchronously practical control is studied for discrete time switched systems with singular perturbations. Firstly, a novel Lyapunov function is constructed including the singular perturbation parameter and quasi-time parameter matrices. And then, quasi-time dependent criteria are achieved to study the practical stability and asynchronous stabilization; an allowable upper bound is expected to be obtained for the singular perturbation parameters; the asynchronous sampling controller is designed with quasi-time gains, and the application range of this controller is further widened via some constraints relaxed. At last, two simulation examples are utilized to illustrate that the proposed results are less conservative and effective.</p>