Robust L2-L∞ guaranteed cost filter for a class of uncertain systems with distributed delays

In the paper, the robust L₂-L_∞ guaranteed cost filter problem of a class of uncertain time-delay systems with distributed delays is considered. Both distributed delays and dependent delays appear in this systems, and the uncertainties are assumed to be norm-bounded. The aim is to design a robust L₂-L_∞ guaranteed cost filter and to obtain upper bound of the quadratic cost function. By constructing proper Lyapunov-krasovskii function, the resulting augmented system is robustly asymptotically stable and satisfies the proposed guaranteed cost performance. In terms of stability theory and LMI methods, a sufficient condition of existence of robust L₂-L_∞ guaranteed cost filter is derived and a robust L₂-L_∞ guaranteed cost filter is presented. Finally, a numerical example is shown to demonstrate the usefulness of the proposed techniques.