In this paper, we study the $ (q,m) $ -dichotomy and periodic solutions for Sylvester matrix Volterra integro-dynamic systems defined on arbitrary time scales.By using the vec operator, we transform the original Sylvester matrix system into an equivalent Kronecker product system.We establish the existence and uniqueness of periodic solutions by fixed point theory and functional analysis techniques.The study uses the concept of a $ (q,m) $ -dichotomy, a generalization of exponential dichotomy, to obtain boundedness and periodicity criteria for solutions.The main results include theorems on the uniqueness of bounded and periodic solutions under specific conditions.
