Improved stability criterion for linear systems with two additive time-varying delay

This paper deals with the stability analysis of dynamic systems with two additive time-varying delay. By decomposing one delay interval into multiple subintervals which may be unequal, an appropriate Lyapunov-Krasovskii functional (LKF) is constructed whose each term is not positive definite while the the sum of each term is positive definite. The integral inequality method and the reciprocally convex technique are utilized to deal with the derivative of the LKF. The delay-dependent stability criterion obtained from this method is expressed in terms of the linear matrix inequalities (LMIs) and has less conservatism than some existing ones.