Delay-dependent stability analysis for linear system with time-varying delay: A PAM method

A piecewise analysis method (PAM) is proposed to investigate the stability of linear system with time-varying delay and uncertainties. Different from the existing methods in dealing with the time-varying delay, the whole variation interval of the delay is divided into two subintervals with equal length. Respecting for the delay belongs to different subintervals, new criteria on stability analysis of the time delay systems are obtained by checking the variation of the derivative of the Lyapunov functional in the two subintervals. Then, by using the convexity properties of matrix inequality and some other new analysis techniques, new criteria are obtained for the asymptotical stable of the time delay systems. The given numerical examples show that the derived criteria can lead to much less conservative results than those obtained based on the existing methods.