Reliable Control And Filtering Of Singular Interval Type-2 Fuzzy System

As a common controlled object in engineering applications,it has important research significance to study stability analysis and control performance improvement of nonlinear systems.However,it is difficult to study the nonlinear system directly.Considering that the T-S fuzzy system can approximate a nonlinear system with arbitrary precision,therefore,the stability analysis and control of the nonlinear system can be converted to the stability analysis and control of the T-S fuzzy system.T–S fuzzy models have been extensively applied to deal with nonlinearities and uncertainties in practical plants,which has a wide range of applications in autonomous mobile robots,heating,ventilation,and air conditioning systems and truck–trailer systems.With the rapid development of science and technology,control systems become more complicated.It is inevitable that actuator failures or sensor failures may exist in the systems,which will affect the stability and other performance of the systems.Therefore,it is very important for us to study the reliable cotrol of the systems.This paper considers the synthesis problem of singular interval type two fuzzy systems: control and filtering.The detailed research contents are given as follows:(1)The admissibility analysis and reliable controller design of interval type-2 T-S fuzzy singular system with actuator failures are investigated.In the case of a controller with actuator failure,derive a closed-loop system expression.According to the Lyapunov stability theory,a appropriate Lyapunov-Krasovskii function is constructed.By analyzing the admissibility of the system,sufficient conditions for controller design are obtained.The results are derived in terms of strict linear matrix inequalities.(2)The admissibility analysis and reliable controller design of interval type-2 T-S fuzzy singular system with time-delay and actuator failures are investigated.In the case of actuator failure,derive a closed-loop system expression.To analyze the admissibility of the system,the method of constructing a suitable Lyapunov function and the Jensen inequality to process the time-delay term are used.The strict linear matrix inequalities are obtained,which are the sufficient conditions for controller design.(3)The admissibility analysis and reliable dissipative filtering design of interval type-2 T-S fuzzy singular system with sensor failures are investigated.Derive the expression of the filter error system in the case of the filter with sensor failure.By constructing a appropriate Lyapunov function and considering the dissipative performance of the system,the sufficient conditions for the filter design are solved.The strict linear matrix inequalities are obtained which make the filter error system admissible and strictly dissipative.