Delay-Dependent Robust $H_{\infty}$ Filtering for Uncertain Discrete-Time Systems With Time-Varying Delay Based on a Finite Sum Inequality

This brief is concerned with delay-dependent robust $H_{\infty}$ filtering for uncertain discrete-time systems with time- varying delay. The uncertainty is of convex polytopic type. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent bounded real lemma (BRL) is derived. In combination with a parameter-dependent Lyapunov–Krasovskii functional, which allows the Lyapunov–Krasovskii matrices to be vertex dependent, the obtained BRL is modified into a new version to suit for convex polytopic uncertainties. Neither model transformation nor bounding technique for cross terms is involved. Based on the new BRL, the designed filter is provided in terms of a linear matrix inequality (LMI), which is easily solved by Matlab LMI toolbox. A numerical example is given to illustrate the effectiveness of the proposed method.