Memoryless non-fragile state feedback control of uncertain multiple time-varying delays system with nonlinearity

This paper deals with the problem of non-fragile robust stabilization for uncertain nonlinear multiple time-varying delays system. The parameter uncertainties are assumed to be time-varying norm-bounded appearing in both state and input matrices. The time-delays are unknown and time-varying with known bounds. The non-fragile robust stabilization problem is to design a memoryless non-fragile state feedback controller such that the closed-loop system is robustly stable for all admissible parameter uncertainties. Using the Lyapunov functional method and free-weighting matrices, delay-dependent sufficient condition for the solvability of the problem is established in terms of linear matrix inequality (LMI). Numerical example is provided to show the effectiveness of the proposed theoretical result.