A new finite sum inequality approach to delay-dependent H∞ 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.