New Stability Analysis for Systems with Interval Time-varying Delay via a Delay-fractioning Approach

This paper addresses the problem of stability analysis for linear systems with interval timevarying delay. A general form of the delay-fractioning approach is proposed, which not only takes advantage of all possible information on the delay's lower bound, but also exploits further information between the delay's upper and lower bounds. A new Lyapunov-Krasovskii functional (LKF) is constructed and delay-dependent stability criteria are derived in terms of linear matrix inequalities (LMIs) by using the piecewise analysis method. The convexity of the matrix function is used to avoid the conservatism caused by enlarging the time-varying delay to its upper bound in each subinterval. Numerical examples are given finally to verify the effectiveness of the proposed criteria.