On delay-dependent asymptotic stability of polytopic time-varying systems with delays

This paper is concerned with the problem of asymptotic stability analysis for a class of polytopic linear time-varying systems with constant delays. Four kinds of delay-dependent stability criteria are obtained respectively based on different Lyapunov-Krasovskii functionals that are either dependent on or independent from the time-varying parameters. The obtained stability conditions are expressed in terms of linear matrix inequalities. When deriving the main results, the free-weighting matrix technique and/or Jensen´s integral inequality are applied. The effectiveness of the proposed method is illustrated via a numerical example provided finally.