Sufficient conditions for the stability of a linear stationary system with a matrix depending on a small non-negative parameter are considered. Theorems are formulated and proved, providing easy-to-verify conditions for maintaining the stability of the system under study for all sufficiently small positive values of the parameter. The resulting theorems are used to analyze the stability of charged particle motion in a Penning trap with an additional rotating electric field and a buffer gas. The role of the small parameter in the modeling is played by the damping coefficient, which characterizes the effect of the buffer gas on the particles. The resulting conditions for maintaining stability when adding a buffer gas to the trap can be effectively used to construct stability regions in the space of the trap's main parameters. Using the proven theorems, the trap stability analysis is significantly simplified, since the characteristic polynomial of the system under study at zero parameter contains only even degrees, which effectively halves (from sixth to third in the general case for the trap) the order of the polynomial for which the root location must be analyzed. Examples of various special trap configurations are also considered, for which the use of the obtained theorems makes it possible to find fairly simple analytical expressions that determine the desired stability region.