Stability Analysis And Controller Design For T-S Fuzzy Systems Based On Time-varying Delay Decomposition Approach

In the actual control systems,time delay is always existent,which reduces the control performance to a great extent and even makes the system unstable.On the other hand,the system is always affected by parameter uncertainties and external disturbances,causing the actual system can not be described by the mathematical model accurately.There exists model errors which reduce the control performance.Compared with the traditional control,the fuzzy control could achieve a more accurate control effect without establishing the precise mathematical model of the system.Takagi-Sugeno(T-S)fuzzy model makes use of the local linearization approach to decompose the nonlinear system into several linear subsystems,and synthesizes the linear subsystems through the membership function to form the fuzzy model in the global sense,realizing the approximation of nonlinear system at any precision.This approximate description makes the problem of nonlinear systems could be solved by a more complete linear system theory.T-S fuzzy model provides an effective theoretical analysis approach for the research of nonlinear systems.More recently,the stability analysis and synthesis of time-delay systems have gradually become one of the research hotspots in the field of international control.A large number of research results have emerged,but there is still a large room for improvement.To sum up,this dissertation will carry out research work from the following three aspects:(1)Consider a class of linear systems with time-varying delay.In order to make full use of the time-delay information,an adjustment parameters α(0 <α <1)is introduced to decompose the time delay interval.The existing L-K functionals have been improved by introducing the augmented matrix and the triple integral term.In the process of derivation,the free weight matrix method and Jensen integral inequality method are both utilized,and then a less conservative time delay dependent stability criterion of the linear system is given in the form of LMIs.Finally,two numerical examples are given to verify the validity of the criterion.The upper bound of the maximum delay is obtained by using LMIs Toolbox.The system model is built by using Simulink,and the system state response diagram is obtained to further verify the validity of the stability criterion.(2)Consider a class of nonlinear T-S fuzzy systems with time-varying delay,the delay decomposition approach is also utilized.Based on the introduction of the augmented matrix and triple integral terms,a quadruple integral term is added to further make full use of the time-delay information,so an improved L-K functional is obtained.A less conservative delay dependent stability criterion of the T-S fuzzy system is given in the form of LMIs.At last,two numerical examples are given to verify the validity of the stability criterion.Through simulation,the validity of the stability criterion in this chapter is further verified.(3)After the research of the stability of nonlinear time-varying delay system based on T-S fuzzy model,the problem of parameter uncertainties and external disturbances is considered.The robust H_∞ stability analysis and controller design of uncertain T-S fuzzy time-delay system are carried out.The delay dependent robust H_∞ stability criterion and the design of fuzzy controller are given in the form of LMIs.Finally,two examples are given to verify the validity of the stability criterion and the feasibility of the robust H_∞ controller design respectively.