A Floquet-Lyapunov Theory for nonautonomous linear periodic differential equations with piecewise constant deviating arguments

Abstract: We present a version of the classical Floquet-Lyapunov theorem for $\omega-$periodic nonautonomous linear (impulsive and non-impulsive) differential equations with piecewise constant arguments of generalized type (in short, IDEPCAG or DEPCAG). We have proven that the nonautonomous linear IDEPCAG is kinematically similar to an autonomous linear ordinary differential equation. We have also provided some examples to demonstrate the effectiveness of our results.