Delay-dependent<b><i>H</i></b>_∞control of linear discrete-time systems with an interval-like time-varying delay

The free-weighting-matrix approach is developed to study the H ∞ control of linear discrete-time systems with an interval-like time-varying delay. First, a delay- and range-dependent criterion for a given H ∞ performance is derived. Second, a memoryless H ∞ state-feedback controller is designed based on a performance analysis. Finally, two numerical examples demonstrate the effectiveness of the proposed method and show that both the upper bound and range of an interval-like time-varying delay affect the stability and/or H ∞ performance of a system. Keywords: Discrete-time systemsTime-varying delayStabilising H ∞ controlLinear matrix inequality (LMI) Acknowledgements This research work was supported in part by the National Science Foundation of China under Grant Nos. 60425310 and 60574014, the Program for New Century Excellent Talents in University, the Doctor Subject Foundation of China under Grant No. 20050533015; and the Hunan Provincial Natural Science Foundation of China. The research work of Qing-Long Han was supported in part by Central Queensland University for the Research Advancement Awards Scheme Project 'Robust Fault Detection, Filtering and Control for Uncertain Systems with Time-Varying Delay' (January 2006 to December 2008).