Research On H_? Control For Nonlinear Systems Based On Fuzzy Lyapunov Function

With the rapid development of science,the fuzzy control technology has been successfully applied in the control theory and engineering practice.Especially,since Takagi and Sugeno proposed the Takagi-Sugeno(T-S)fuzzy model,many scholars have done extensive research on the stability analysis and control synthesis of nonlinear systems based on this model.Most of the existing results are based on the common quadratic Lyapunov function and the parallel distribution compensation(PDC)algorithm,which makes the result conservatism to a certain extent,and the fuzzy Lyapunov function can obtain a less conservative result than the quadratic Lyapunov function.Therefore,on the basis of predecessors,based on fuzzy Lyapunov function and linear matrix inequality(LMI)technology,the H? control problem for a class of nonlinear systems described by T-S fuzzy model are further discussed in this paper.The contents are as follows:(1)The problem of stabilization and H? controller design for a class of continuous-time T-S fuzzy systems are studied,by constructing a less conservative fuzzy Lyapunov function,using PDC algorithm,introducing more relaxed matrix variables and taking fully consideration of the time derivative of membership functions,a new less conservative stabilization condition is obtained.Further,the H? controller design method of the system is given.(2)The problem of robust stabilization and robust H? control for a class of uncertain fuzzy systems with input constraints are discussed.First,based on an improved fuzzy Lyapunov function,using non-parallel distributed compensation(non-PDC)control laws,the robust stabilization condition and robust H? controller design method without input constraints are obtained.Then,the problem of robust H? control with input constraints is discussed.The proposed approach does not need additional requirements for the time derivative of membership functions.Compared with the quadratic Lyapunov function,the designed H? controller obtains a smaller disturbance attenuation level.(3)For a class of continuous nonlinear Markov jump systems with parameter uncertainties,external disturbances and unmeasurable states,the observer-based robust H? control problem is studied.First,considering that there are no parameter uncertainties and unmeasurable states of the system,by constructing a mode-dependent fuzzy Lyapunov function,using PDC algorithm and introducing slack matrix variables,the stochastic stabilization and H?performance analysis method of the system are given.Then,considering the existence of uncertainties and unmeasurable states of the system,a state observer and feedback controller are constructed to reconstitute the system into an augmented system,based on mode-dependent fuzzy Lyapunov function,using matrix contract transformation and LMI technology at the same time,and the observer-based robust H? control approach is obtained in the forms of LMI.