This paper addresses the problem of designing a robust controller for a class of nonlinear systems whose states cannot be precisely measured caused by the unknown drifts in the powers of the measurement functions. By adopting the concept of homogeneity with monotone degrees and revamping the technique of adding a power integrator, a new design procedure is introduced to recursively construct a generalized homogeneous controller with monotone degrees as well as a Lyapunov function with unknown parameters. The proposed controller is able to globally stabilize a family of nonlinear systems with different measurement drifts whose bounds can be determined by solving an optimization problem. (C) 2016 Elsevier Ltd. All rights reserved.