Improved delay-dependent stabilisation criteria for discrete systems with a new finite sum inequality

This study introduces a new finite sum inequality to investigate the problem of delay-dependent stability analysis and controller synthesis for a discrete system with an interval time-varying input delay. By constructing a novel piecewise Lyapunov–Krasovskii functional and employing the proposed finite sum inequality to deal with sum items in the derivation of our results, simplified whereas improved delay-dependent stabilisation criteria are obtained with the less number of linear matrix inequalities scalar decision variables. Numerical examples show the effectiveness of the proposed method.