New delay-dependent criteria with fewer decisive variables for linear systems with interval time-varying delays

摘要

This note deals with the stability problem of linear system with time-varying delay in a given range. In order to analyze its stability, a new type of Lyapunov functional (LF) which incorporates more information on the delay and some triple-integral terms is constructed. By combining Jensen's integral inequality with a delay division technique, upper bound of LF derivative has been estimated more tightly and expressed as a convex combination with respect to a tuning parameter. New stability criteria with fewer decisive variables but less conservatism are derived in terms of linear matrix inequalities (LMIs). Numerical examples authenticate the effectiveness of the proposed method.