Control Of Nonlinear Systems Based On T-S Fuzzy Hyperbolic Model

Fuzzy logic system utilizing fuzzy sets and fuzzy inference to process uncertain information which cannot be represented accurately by mathematical tools, the study of complex nonlinear systems has had a great breakthrough. Therefore, fuzzy control theory and methods based on fuzzy logic system become one of the core of the control. With the constantly improvement of the T-S fuzzy control theory, T-S fuzzy linear system theory, T-S fuzzy bilinear system theory, and T-S fuzzy nonlinear system theory were successively proposed. Besides, T-S stochastic fuzzy system, T-S fuzzy sampled-data control and non-fragile control are researched in this paper.Based on T-S fuzzy hyperbolic system, according to Lyapunov stability theorem, Schur complement theorem, linear inequality(LMI) techniques, and non-fragile guaranteed cost control, T-S stochastic fuzzy hyperbolic model and T-S sampled-data fuzzy hyperbolic model are respectively proposed to research the nonlinear stability. The main contributions can be generalized as follows:Firstly, a novel T-S stochastic fuzzy hyperbolic model is presented for a class of continuous nonlinear, the consequence of which is a hyperbolic tangent dynamic model. First, according to PDC the fuzzy hyperbolic controller of T-S stochastic fuzzy hyperbolic system is designed. The stability conditions of the closed-loop system are derived via linear matrix inequalities(LMI). Then, combining with T-S fuzzy output –feedback controller, the stability analysis of T-S stochastic fuzzy hyperbolic system with output feedback controller is studied. Third, the model is promoted to T-S uncertain fuzzy system. Comparing with the control method of the other T-S fuzzy system, the novel control method may achieve much smaller control amplitude in the case of the state stabilization time which is almost the same, and it can be referred to as “soft” constraint control approach.Secondly, the design of sampled-data guaranteed cost fuzzy hyperbolic control is investigated for a class of nonlinear systems with control input constraints and the time-varying sampling way, where the nonlinear systems are described by continuous time T-S fuzzy hyperbolic models. Considering the control input constraints, a new lemma is presented to obtain the deviation bounds of the membership functions in the sampled-data fuzzy hyperbolic control system and to establish a quantitative relation between the deviation bounds and the upper bound of time-varying sampling intervals. Then, a membership function deviation approach is proposed to design the sampled-data fuzzy hyperbolic controller, and the membership function deviation dependent condition for the existence of the sampled-data fuzzy hyperbolic controller is derived in terms of LMIs. Besides, the method is extended to the non-fragile guaranteed cost hyperbolic controller and the stability conditions are obtained. Finally, it is shown numerically that the proposed membership function deviation approach can reduce the conservativeness of some existing results in the field of sampled-data fuzzy hyperbolic control design.