On Qualitative Behaviour of Solutions of Third Order Matrix Delay Differential Equations

We analyze, using the Lyapunov-Krasovskii method, the conditions for the stability, boundedness and periodicity of solutions to a class of nonlinear matrix differential equation of third order with variable delay. Criteria under which the solutions to the equation considered possess solutions that are stable and bounded on the real line as well as existence of at least one periodic solution are given. Our results generalize and extend many existing results in the literature on scalar, vector and matrix differential equations with or without delay. The integrity of our results is demonstrated by two numerical examples included.