A new robust feedback controller for the safety factor profile and poloidal plasma pressure parameter has been developed using a two-time-scale data-driven model. The model describes the linear plasma responses of the ι profile and βp with respect to auxiliary heating & current drive (H&CD) powers, around a typical plasma equilibrium in an H-mode steady-state plasma discharge on EAST. The feedback controller comprises a carefully designed low-pass filter for the timescale separation, a decoupling module and three local controllers synthesized from the ℋ∞ norm optimization and the singular value decomposition. The actuators are the lower hybrid current drive (LHCD) system at 4.6 GHz and the ion cyclotron resonance heating (ICRH) system at 33 MHz. Taking into account the actuation dynamics, an anti-windup technique is employed to condition the controller online aiming to attenuate the negative effects from moderate time delays and power saturations. Extensive nonlinear closed-loop simulations with the METIS code suggest that high βp and negative central magnetic shear that characterize advanced tokamak plasma scenarios can be achieved and sustained on EAST with good tracking performance and reasonable robustness via the proposed control scheme. The feedback control of the core ι profile and βp with a range of time delays, power saturations and varying weighting functions are evaluated numerically, compared and discussed. The control robustness to plasma parameter uncertainties including the line-averaged plasma density 〈ne〉, the H-mode enhancement factor Hfactor and the effective charge number Zeff are assessed and analyzed.