Generalized H<inf>2</inf>Control of Linear Neutral Time-delay Systems

Abstract

This paper considers the generalized H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> 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 <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> 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 <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> index for linear neutral time-delay systems, proposes a sufficient condition of the existence of L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> control for this kind of system and provides the design of the optimal L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -L∞ 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.