Finite-time Bounded Control For Continuous-time T-S Fuzzy System

With the rapid development of industrial society,the control requirements for nonlinear complex systems are becoming increasingly diverse.The T-S fuzzy model,due to its good approximation characteristics,is one of the powerful tools for dealing with nonlinear systems.Therefore,it has been widely used in modeling and control of nonlinear systems,and has achieved fruitful results in related research such as system stability analysis and control synthesis.However,in certain application scenarios such as blood gas control during extracorporeal circulation processes,considering the dynamic performance requirements of the system,it is more necessary to achieve stability and robustness of the system within a limited time interval.Therefore,using T-S fuzzy systems to study the finite-time control problem of nonlinear complex systems is of great significance.This article focuses on the finite-time control problem of nonlinear systems,establishes its T-S fuzzy model,designs a fuzzy Lyapunov function,and proposes a new control synthesis method based on linear matrix inequality methods.The main research contents are as follows:(1)The finite-time H_∞control problem is studied for continuous-time T-S fuzzy system with bounded disturbances.Firstly,the T-S fuzzy model for the blood gas control system is established and a fuzzy controller based on state observer is designed.Secondly,unlike existing literature,sufficient conditions with smaller conservativeness for bounding the time derivative of membership functions are obtained based on fuzzy Lyapunov function.Furthermore,by applying Finsler’s lemma and matrix decoupling technique,a set of sufficient conditions are given to ensure that the system satisfies H_∞finite-time boundedness.The simulation results show that the designed controller can effectively estimate the system state and meet the design requirements.(2)The H_∞finite-time bounded control problem is studied for T-S fuzzy system with uncertain parameters.Considering the fact that actual systems not only face external disturbances,but also changes in their own structure and parameters can have a significant impact on the control system.Firstly,a non-fragile controller with gain disturbance is designed and a set of sufficient conditions that satisfy H_∞finite-time boundedness is provided.Secondly,based on existing literature,a new scaling method is adopted to handle the time derivative of membership functions,and a set of conditions with less conservatism that restrict the membership functions are obtained.In addition,utilizing matrix transformation techniques,a new set of conditions with less conservatism is developed for designing fuzzy controllers with gain perturbations.Finally,simulation verifies the effectiveness of the proposed design method.