The fragility defect of the existing prescribed performance control (PPC) is discussed. Based on this, the basic conception of nonfragile PPC is proposed. Firstly, the basic framework and key technologies of PPC are briefly summarized. Then, the possible control singular problem caused by actuator saturation and disturbance of the existing PPC is systematically analyzed, the fragility problem of the existing PPC is pointed out, and the main idea of the nonfragile PPC methodology and three basic problems (i.e.,error sensing,envelope adjustment and prescribed performance guarantee) that should be solved are given. Finally, based on the basic conception of non-fragile PPC, feasible implementation schemes of which are presented, and the superiority is verified via compared simulations. The relevant researching results are able to make up for the fragility defect of PPC and also are beneficial for opening up the new research field of non-fragile PPC.