A less conservative stability condition of time-delay systems with polytopic uncertainty

This paper considers the problem of stability analysis of time-delay systems with time-varying delay. By introducing a small scalar, the products between system matrices and Lyapunov matrices are decoupled with the help of the introduced additional matrices. Therefore, when the time-delay systems with polytopic uncertainties are investigated, the vertex-dependent Lyapunov function can be allowed, and thus the conservativeness can be reduced. Numerical examples are given to verify the effectiveness of the proposed results.