This paper proposes a novel control method for a special class of nonlinear systems in semi-strict feedback form. The main characteristics of this class of systems is that the unmeasured internal states are non-uniformly detectable, which means that no observer for these states can be designed to make the observation error exponentially converge to zero. In view of this, a projection-based adaptive robust control law is developed in this paper for this kind of system. This method uses a projection-type adaptation algorithm for the estimation of both the unknown parameters and the internal states. Robustifying feedback term is synthesized to make the system robust to uncertain nonlinearities and disturbances. It is theoretically proved that all the signals are bounded, and the control algorithm is robust to bounded disturbances and uncertain nonlinearities with guaranteed transient performance. Furthermore, the output tracking error converges to zero asymptotically if the system has only parametric uncertainties. The class of system considered here has wide engineering applications, and a practical example - control of mechanical systems with dynamic friction - is used as a case study. Simulation results are obtained to demonstrate the applicability of the proposed control methodology.