This paper addresses the design of a covert attack on a linear multivariable dynamical system with input hard constraints. The system evolves in the discrete-time domain and is subject to performance and alarm state constraints, both represented by convex and compact polyhedral sets. A contractive control law guarantees positive invariance of the performance set, while ensuring asymptotic stability of the origin with maximum convergence rate. An attacker succeeds in gaining control of the system and sends false control commands, when it is necessary, eventually driving the state vector outside the performance set without violating any alarm constraints. Simulation studies highlight the results of this adversary control scheme.