To understand the impact of cyber-attacks to sensors in control systems, we present a stability analysis of a wide range of systems in this paper. Based on Lyapunov stability analysis, we formulate an optimization problem with constraints in the form of a set of linear matrix inequalities to find conservative bounds of stability related to the attacks, which can be analyzed simultaneously or one at the time. When considering the attacks one at the time, with the proposed formulation, we can find the most vulnerable output in the system, which can help the designer (i.e., the defender) to understand how to make the system more secure in case of multiplicative attacks on sensors. We show the effectiveness of our analysis with simulations based on the three tanks benchmark system.