Improved Robust Stabilization of Time-Delay Systems via Fuzzy Discretized Approach

This paper investigates the problem of stabilization of linear systems with unknown delay. The delay term in the system is represented by an interpolation of state values with constant delays by fuzzy approximation technique, resulting in a fuzzy model describing a large amount of complex systems focused on the unknown delay, where the delay can be constant and time-varying with or without known delay derivative. Based on the model, a new fuzzy model-based approach incorporating with the fuzzy discretized Lyapunov functional method is proposed for solving the stabilization problem, inspired by the discretized Lyapunov functional method \cite{Gu2001} which is used to deal with the stability analysis for constant delay case, and with the help of slack matrix techniques, improved stabilization conditions are obtained in terms of linear matrix inequality with less conservatism than some results in the literatures. Finally, a simulation example is provided to shown the less conservatism of the obtained results.