Estimating delay bounds of time-delay systems with fuzzy model-based approach

This paper aims at estimating the delay bounds of linear systems with unknown state delay via a novel fuzzy model-based approach. Both robust stability analysis and stabilization problems are investigated with the estimation. Fuzzy techniques are utilized novelly by setting the time-varying delay to be distributed on the fuzzy set, and a novel fuzzy model is proposed to describe the linear time-delay system, where the state with time-varying delay is represented by an interpolation of states with some local constant delays. Based on the model, a new approach incorporating with the developed fuzzy discretized Lyapunov functional and slack matrix techniques is presented, and new stability criteria of time-delay systems are obtained. Further, the controller design method is developed to guarantee the asymptotic stability of the closed-loop system. The obtained stabilization conditions developed by the proposed fuzzy model-based approach are much less conservative than those obtained by the traditional methods in some literature. The results are presented in the form of linear matrix inequality, which can easily be solved by standard software packages. Simulation examples are provided to show the less conservativeness and effectiveness of the obtained results.