Abstract: The uncertainties were described as timevarying parameter vectors belonging to a hyper rectangle. The problem of exponential stability for uncertain linear discretetime systems with timevarying delays was investigated by using affine parameterdependent Lyapunov functional. Exponential stability was guaranteed by the exponential decay of the Lyapunov functional. Affine parameterdependent freeweighting matrices were introduced to analyze the exponential decay of the Lyapunov functional， and the matrix inequalities containing timevarying parameters were transferred to linear matrix inequalities by using the properties of multiconvex function. Therefore， a sufficient condition for exponential stability was obtained. Since the information of upper and lower bounds of the uncertain timevarying parameters and their increments was effectively used and the convex combination method was applied when handling interval timevarying delay， the proposed method had less conservatism. An example was presented to show the effectiveness of the proposed method.

Key words: timevarying delay, discretetime system, exponential stability, uncertain parameters, linear matrix inequalities