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

This paper is concerned with the problem of delay-dependent H-infinity control for linear 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 is asymptotically stable (internally stable) with a prescribed H-infinity attenuation level via a memoryless state feedback. Then, an iterative algorithm involving convex optimization is proposed to obtain a suboptimal H-infinity controller. Finally, a numerical example is given to show the effectiveness of the proposed method.