A new finite sum inequality approach to delay-dependentH∞ control of discrete-time systems with time-varying delay

This paper deals with delay‐dependent H ∞ control for discrete‐time systems with time‐varying delay. A new finite sum inequality is first established to derive a delay‐dependent condition, under which the resulting closed‐loop system via a state feedback is asymptotically stable with a prescribed H ∞ noise attenuation level. Then, an iterative algorithm involving convex optimization is proposed to obtain a suboptimal H ∞ controller. Finally, two numerical examples are given to show the effectiveness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.