Simplified descriptor system approach to delay-dependent stability and performance analyses for time-delay systems

Simplified delay-dependent asymptotic stability conditions are provided for time-delay systems in terms of linear matrix inequalities. The redundant variables in the previous results derived by the so-called ´descriptor system approach´ together with recently proposed bounding techniques are removed. Thus, the newly proposed conditions are equivalent to these obtained by the descriptor system approach but with reduced complexity. It is shown that the bounding technique does not have to be used in the derivation of our results. By the proposed method, delay-dependent results on H_∞ performance analysis for time delay systems are also presented.