Delay-dependent H ∞ control of linear discrete-time systems with an interval-like time-varying delay

Abstract

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.