Stability analysis of linear time-invariant difference-differential system with constant and distributed delays

Abstract We investigate the conditions under which a diagonal solution exists for a linear matrix inequality that arises when studying the asymptotic stability of differential-difference systems with both discrete and distributed delays. Our primary contribution is the characterization of the existence of positive definite diagonal matrices that ensure the asymptotic stability of these systems through Lyapunov-Krasovskii functionals. We establish several necessary and sufficient conditions for the existence of such positive definite diagonal solutions and extend recent results related to positive systems with difference-differential equations.