Robust delay-dependent stability of polytopic systems with interval time-varying delay

This paper concerns the problem of robust stability analysis for a polytopic system with interval time-varying delay via parameter-dependent Lyapunov functions. By a relaxation approach with slack matrices and a descriptor model transformation of the system, the product between Lyapunov variables and the system matrices is eliminated. With this feature, a delay-dependent robust stability criterion is expressed as a set of linear matrix inequalities (LMIs). Compared with the results based on parameter-independent Lyapunov functions, this is promising for less conservatism. Two numerical examples are included to illustrate the effectiveness of the proposed method.