This article provides control theory methods to analyse, prevent, and assess the feasibility of stealthy ageing attacks on controlled physical systems, modelled as dynamical systems. This new type of attacks leads to premature failures of the physical system by accelerating its ageing and remains stealthy by maintaining the system outputs as in the attack‐free case. An attacker with restrained capabilities is considered: it can only corrupt the control signals transmitted to the dynamical system. This article provides set‐theoretic methods to analyse and prevent these attacks by restraining the control signals in amplitude, whether the system is stable or not. The proposed methods consist in solving optimisation problems under Linear Matrix Inequality constraints. Then, a method based on linear programming is proposed to assess the feasibility of such attacks by finding the optimal attack control signals. At the end of this article, the methods are applied on two application examples to show their relevances: a thin film manufacturing and a satellite reorientation manoeuvre.