This paper investigates the tracking control problem of a class of multi-input multi-output (MIMO) nonlinear systems under asymmetric full-state constraints. By integrating a nonlinear transformed function (NTF) with the upper bound estimation technique, we develop a robust adaptive dynamic surface control (DSC) method that exhibits several attractive features: 1) both symmetric and asymmetric state constraints are directly addressed without the need for converting the state constraints into new constraints on tracking errors (as used in the Barrier Lyapunov Function (BLF) in most existing works). Such control scheme (with its structure unchanged) is also applicable to the systems free from state constraints; 2) the undesirable feasibility conditions on virtual control laws commonly involved in most existing works are completely eliminated; and 3) the utilization of NTF-based DSC and upper bound estimation technique not only avoids the explosion of complexity problem in traditional backstepping design, but also allows a structurally simple and computationally inexpensive control scheme to be developed, in which only one single parameter updating is needed, significantly reducing the design complexity and online computation. The effectiveness of the proposed scheme is verified via simulation. (C) 2019 Elsevier Ltd. All rights reserved.