Generalized H2Control of Linear Neutral Time-delay Systems

This paper considers the generalized H₂ 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 H₂ 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 L₂ - Lprop index for linear neutral time-delay systems, proposes a sufficient condition of the existence of L₂ - Lprop control for this kind of system and provides the design of the optimal L₂ - Lprop 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