Joint congestion control and link scheduling has been proposed as an approach to fair resource allocation in wireless networks. Existing solutions usually favor a distributed cross-layer deployment that requires timely communications among network components in seeking system stability and global optimum. However, this is unrealistic with feedback delay and channel capacity perturbation. The stability and efficiency of these algorithms face significant challenges. In this paper, we present a robust joint congestion control and scheduling algorithm, i.e., ROCS, for time-varying multi-hop mesh wireless networks with feedback delay, to bridge the gap between the existing approaches and the reality of wireless networks. The fundamental idea behind ROCS is capacity space projection, which combines the slow time scale part of the channel capacity and a margin estimated from the fast time scale part, to form a new capacity space. The resource allocation problem is formulated into a utility maximization framework over the newly generated capacity space. The problem is solved by a control algorithm consisting of link scheduling and congestion control. Link scheduling coordinates wireless link utilization, and congestion control allocates flow rates according to feedback information. Experiments conducted over simulated and real-world traces demonstrate that ROCS substantially achieves robustness and efficiency.