A delay decomposition approach to stability and H<inf>∞</inf> control of linear time-delay systems — part II: H<inf>∞</inf> control

This paper is concerned with H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> control for linear time-delay systems. Delay-dependent bounded real lemmas (BRLs) are established by using a delay decomposition approach. Employing the obtained BRLs, some delay-dependent sufficient conditions for the existence of memoryless and delayed state feedback controllers, which ensure asymptotic stability and a prescribed H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> performance level of the corresponding closed-loop system, is formulated in terms of a linear matrix inequality (LMI). A practical example is given to illustrate the effectiveness of the design method.