Generalized H2 control of linear neutral time-delay systems

This paper considers the generalized H-2 control problem of linear neutral time-delay systems. The linear neutral time-delay system can be viewed a kind of hybrid systems, since it is a difference-differential system. So it can include the linear time-delay system, and has its own characteristic. Through studying the generalized H-2 control problem, we wish to provide a new way to study the linear neutral time-delay systems. By Lyapunov-Krasovskii functions, this paper applies the LMI technology to give a criterion of L-2 - L-proportional to index for linear neutral time-delay systems, proposes a sufficient condition of the existence of L-2 - L-proportional to control for this kind of system and provides the design of the optimal L-2 - L-proportional to controller for the linear neutral time-delay systems. The result of this paper can be applied to study the uncertain linear neutral time-delay systems. A numerical example shows the potential of the method proposed in this paper.