Robust generalized H2 control of linear neutral systems with time-varying delay

This paper considers the robust GH(2) control problem of linear neutral systems with time-varying delay. The linear neutral time-delay systems can be viewed a kind of hybrid systems, since this kind of systems can be described as difference-differential form. So this kind of system can include the linear time-delay system, and has its own characteristics. Through studying the robust GH(2) control problem, we wish to provide a new way to study the linear neutral time-delay system. By Lyapunov-Krasovskii functions, this paper gives a criterion of L-2-L-infinity performance index for uncertain linear neutral time-delay systems with time-varying delay in LMI form, proposes a sufficient condition of the existence of L-2-L-infinity controller for this kind of system by solving the flexible problem of a group of LMI inequalities, and provides the method of designing the optimal L-2-L-infinity controller for the uncertain linear neutral time-delay systems with time-varying delay. A numerical example provided shows the potential of the method proposed in this paper.