A Lyapunov functional for a neutral system with a distributed time delay

In this paper a Lyapunov functional determination method for a linear neutral system with both lumped and distributed time delay is formulated and solved. A form of a Lyapunov functional is assumed and a computing method of its coefficients is given. The Lyapunov functional is constructed for a given time derivative which is calculated on a trajectory of a neutral system with both lumped and distributed time delay. The presented method gives analytical formulas for the Lyapunov functional coefficients. An example illustrating the application of discussed theory is presented.