Controller Design For Discrete-time Interval Type-2 Fuzzy Bilinear Systems

Fuzzy control model is one of the effective methods to study complex nonlinear systems,and the related research results have been widely used in modernization construction.The interval type-2 fuzzy control model provides a new way for further study of nonlinear systems with uncertain parameters.Based on the Lyapunov stability theory and some new matrix inequalities,the problems of stability analysis,controller design,dissipative control and observer design for discrete-time interval type-2 fuzzy bilinear systems have been studied in this thesis.Some new stability theories and controller design methods are obtained as following:The first part is concerned with the design of state-feedback controller for discrete-time interval type-2 fuzzy bilinear systems with constant delay.Based on the Lyapunov stability theory,an interval type-2 fuzzy state-feedback control criterion is proposed,and the sufficient conditions for the stability of discrete-time interval type-2fuzzy closed-loop bilinear systems are obtained.One numerical simulation example is introduced to demonstrate the correctness and effectiveness of the results.In the second part,the problem of strictly dissipative stability for a class of discrete-time interval type-2 fuzzy bilinear systems with infinite-distributed delays and external disturbances is investiagted.By designing fuzzy bilinear static-output-feedback controller,the closed-loop system is strictly dissipative stable in the range of allowable parameters.The fuzzy controller can be obtained by using sequential linear programming matrix method.Finally,one example is introduced to demonstrate the effectiveness of the results.In the third part,considering that the system's states and inputs can not be completely measurable,based on the fuzzy bilinear observer,the stability of the discrete-time interval type-2 fuzzy bilinear systems with time-varying delays is investiagted.Based on the Lyapunov function method and using advanced matrix inequality,the double and triple difference items which are often ignored are considered in the derivation of the Lyapunov functions,and the sufficient conditions for the stability of the augmented system are obtained.One numerical simulation example is introduced to demonstrate the effectiveness of the results.