  In this work, we consider the periodic impulse control of a system modeled as
a set of linear differential equations. We define a matrix that governs the
qualitative behavior of the controlled system. This matrix depends on the
period and effects of the control interventions. We investigate properties of
the spectral radius of this matrix and in particular, how it depends on the
period of the interventions. Our main result is on the convexity of the
spectral radius with respect to this period. We discuss implications of this
convexity on establishing an optimal and maximum period for effective control.
Finally, we provide an example motivated from a real-life scenario.

Optimization and Control;Spectral Theory;Quantitative Methods