A New finite sum inequality for delay-dependent H∞ control of discrete-time delay systems

This paper is concerned with the problem ofdelay-dependent H∞ control for linear discrete-time systems with time-varying delay. A new finite sum inequality is first established to derive a delay-dependent condition, underwhich the resulting closed-loop system is asymptoticallys table (internally stable) with a prescribed H∞ attenuation level via a memoryless state feedback. Then, an iterative algorithm involving convex optimization is proposed to obtain a suboptimal H∞ controller. Finally, a numerical example is iven to show the effectiveness of the proposed method.