Study Of H_∞ Robust Control For A Class Of Time Delay Uncertain Systems

We can hardly obtain accurate mathematics model for the practical control objects, during analysis and study on control systems. The model we obtained is just an approximate model owing to order reduction; linearity approximations; measurement errors; immeasurable disturbances. Usually,these differences can be described as the uncertainties in the model arguments. On the other hand, time-delay, which leads to non-stabilization and decline of dynamic performance, exist in many systems such as steel rolling, transmission process, and network signal transmission et al. Therefore the study of the uncertainty systems with time-delay has theoretic and practical significance, and has attracted considerable attention in the control theory literatures.Presently, although there are many results about these problems, lots new problems still needs much study and research. In this dissertation, based on Lyapunov stability theory, through using linear matrix inequality and matrix analysis as main mathematical tools, we studies the robust H_∞control problem of uncertain discrete time delay system described by fuzzy model and uncertain systems with multiple time delay. The major contributions are as follows:(1) Study the control problem of discrete time delay uncertain system described by T-S fuzzy model. A sufficient condition for the solvability of the fuzzy guaranteed cost and H_∞robust control problem was presented and proved by applying a proper Lyapunov function and linear matrix inequality. A fuzzy H_∞robust controller which satisfies proper performance was designed.(2) Deal with a problem of a class of complex uncertain system with multiple time delay under controller gain perturbations—additive and multiplicative. A sufficient condition for the solvability of the non-fragile H_∞robust control problem is proved and presented by applying proper Lyapunov function and linear matrix inequalities (LMIs). The non-fragile H_∞robust controller is designed.