Stability Analysis And Stabilization Of Fuzzy Parameter Varying Systems

Although the research on the T-S fuzzy system control theory is becoming more and more good,it is often limited to apply the control method to practical engineering.The main reason is that when there are too many time-varying parameters in the system,the number of predecessor variables and subsystems increases,and the number of linear ma-trix inequalities will increase exponentially with the number of time variable parameters and the precision requirements.The dissertation proposes and studies the fuzzy param-eter varying system theory for the problem that the number of rules increases when T-S fuzzy models deal with time-varying systems.The fuzzy parameter varying system is a new nonlinear time-varying model integrating the advantages of T-S fuzzy systems and linear parameter varying systems.It not only inherits the advantages that T-S fuzzy sys-tem can effectively deal with nonlinear systems,but also expands the application scope of the linear parameter varying theory.According to the design idea of parallel compensation controller based on quadratic Lyapunov function in traditional T-S fuzzy model theory,the dissertation presents a par-allel compensation controller design method for fuzzy parameter varying systems.The optimization theory is used to obtain the design conditions of the controller containing fi-nite linear matrix inequalities.Inspired by the theory of adaptive control,this dissertation also gives a parameter dependent full state feedback controller based on quadratic Lya-punov function and an output feedback controller design method that can be applied to practical systems.In addition,the parameter dependent controller design method present-ed in this dissertation provides better inducement of the L₂norm performance compared to the results that are based on the quadratic Lyapunov function in the classical T-S fuzzy system theory.In order to further cut down the conservativeness,the fuzzy Lyapunov function is applied in the dissertation.The complete block S-procedure lemma is used to separate the quadratic term and the cross term of the membership function and the time-varying parameter,and the non-convex problems are transformed into convex problems of linear matrices inequalities.In order to make full use of the information of the membership function,the technique of scaling the matrix is also introduced to reduce the conservatism caused by the constraint of derivative term of membership functions.Finally,a parameter dependent gain scheduling state feedback and output feedback controller design methods based on fuzzy Lyapunov function are presented.Considering the time-varying parameter online measurable property,the parame-ter dependent Lyapunov function is introduced to reduce the conservation of the results based on the quadratic Lyapunov function.According to the different conditions that the known parameters are satisfied,the several different stability criteria of fuzzy parameter varying systems are given.In view of the theory of linear parameter varying system con-trol and the idea of gain scheduling control,we give the controller design method of the gain scheduling state feedback and output feedback based on the parameter dependent Lyapunov function by making full use of time-varying parameter information,applying convex optimization techniques and multiple full block S-procedure lemma.Finally,the above proposed control methods are applied to the trajectory tracking control of the Mars probe into the Martian atmosphere in order to verify the effective-ness of them.Taking the atmospheric density of Mars as a time-varying parameter,we establish its corresponding fuzzy parameter varying model,and design the parameter de-pendent H_?controller based on the quadratic,fuzzy and parameter dependent Lyapunov functions.Numerical simulation results show that the three control methods can make the Mars probe enter the Martian atmosphere according to the pre-designed trajectory.