Delay Fuzzy Systems Multi-objective Control

Fuzzy logic control technique,as one of the most effective approaches to controlling complex systems which are mathematically poorly modeled,has received considerable attention during the past decades.In the light of recent work in Takagi-Sugeno(T-S)delayed fuzzy systems and with the intensive study on both the time-delay systems and fuzzy systems, this dissertation provides a systematic study on the theory of multi-objective control for T-S delayed fuzzy systems.Firstly,the problem of H₂/H_∞control is investigated;fuzzy state feedback controllers are designed to guarantee the closed-loop system is asymptotically stable and satisfies a prescribed H₂/H_∞performance level.In the case when not all states are available for feedback,the problem of H₂/H_∞control via dynamic output feedback controllers is addressed;.a sufficient condition for the solvability of the problem is provided.This dissertation also deals with the H_∞/L₂-L_∞control problem for a class of T-S delayed fuzzy systems.By the Lyapunov stability theory and the techniques on matrix transformation,fuzzy state feedback controllers are designed such that the closed-loop system is asymptotically stable while ensuring a prescribed H_∞/L₂-L_∞performace level.Finally,the problem of H₂/H_∞control for a class of discrete T-S delayed fuzzy systems is considered;a sufficient condition for the solvability of the problem is obtained and algebraic expressions of desired fuzzy state feedback controllers are also given.It is pointed out that all of the derived conditions guaranteeing the existence of controllers in the dissertation are in terms of a set of linear matrix inequalities.Therefore,desired controllers can be constructed by using the Matlab LMI Control Toolbox to solve certain linear matrix inequalities.