In this dissertation, several new stability analysis techniques and systematic design procedures for the Takagi-Sugeno (T-S) model-based fuzzy control and neural-network-based approach are proposed. This paper also investigates the effectiveness of a passive Tuned Mass Damper (TMD) and fuzzy controllers in reducing the structural responses under the external force. In general, TMD is good for linear system. We proposed here an approach of Takagi-Sugeno (T-S) fuzzy controller to deal with the nonlinear system. In this dissertation, the nonlinear part is concerned with the nonlinear stiffness but not the field of nonlinear plastic behavior of the structural response. To overcome the effect of modeling error between nonlinear systems and T-S fuzzy models, a robustness design of fuzzy control via model-based approach is proposed in this work. A stability criterion in terms of Lyapunov's direct method is derived to guarantee the stability of nonlinear interconnected systems. Based on the decentralized control scheme and this criterion, a set of model-based fuzzy controllers is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear interconnected system and the control performance is achieved at the same time. Also, several asymptotically stability conditions via linear matrix inequalities (LMI) approaches are derived for multiple time-delay nonlinear systems. In this dissertation, neural network (NN) model is employed to approximate the nonlinear systems. Then, the dynamics of each NN model is converted into LDI (linear differential inclusion) representation. Next, a robustness design of fuzzy control via NN-based approach is proposed to overcome the effect of modeling error between nonlinear systems and NN models. Meanwhile, NN model approach is better than T-S fuzzy model to approximate the nonlinear systems. Finally, the developed theory is illustrated by an example of a nonlinear TMD system throughout this paper. Several illustrative examples and simulations are used to demonstrate that the proposed approaches are effective. However, in chapter 6, the practical application in structural system does not discuss the influence of the time delay. Besides, the designing procedures for the T-S fuzzy model and NN model are systematic and simplified.
