Abstract: In this paper, the problem of adaptive stabilization of slowly time-varying systems with unmodeled dynamics is investigated in the presence of unknown but bounded disturbances. The plants under consideration are non-minimum phase and time-varying and contain norm-bounded unmodeled dynamics, and cannot be stabilized by time-invariant robust controller or adaptive controller. A new adaptive robust scheme is proposed based on integration of l1 optimization design methodology and projection algorithm of parameter estimation. Using the continuity properties of l1 optimal control and convergent properties of projection algorithm, the adaptive scheme proposed in this paper can persistently adapt to the time-varying plant to maintain uniform stability. Robustness analysis demonstrates that this scheme has good robust stability.