| Nonlinear systems can be described as a combination of multiple linear subsystems by using membership functions,namely,T-S fuzzy system form.Thus,many mature control theories on linear systems can be used in the control problems of T-S fuzzy systems.Based on the T-S fuzzy model,this dissertation focuses on the stabilization problem of the fuzzy system as follows:Firstly,a parallel distributed compensation controller is designed to establish the closed-loop system for the stabilization problem of the T-S fuzzy system.Then,a Lyapunov function in the form of line integral is selected for carrying out stability analysis of the closed-loop system.And the chosen Lyapunov function is required to satisfy the path-independent constraints.And Bilinear Matrix Inequality(BMI)conditions can be obtained during the stability analysis,and an iterative algorithm is given to derive its solutions.Finally,a simulation example is used to verify that the line integral Lyapunov function gives a larger domain of stabilization compared to the quadratic Lyapunov function.Secondly,a new parallel distributed compensation controller containing the definite integral of the membership function is designed to establish a closed-loop system for the stabilization control problem of T-S fuzzy system.Then,through the equivalent substitution of the relevant parameters in the line integral Lyapunov function,a fuzzy-like Lyapunov function containing the definite integral of the membership functio n is obtained for the stability analysis of the closed-loop system.During the analysis,the numerical information of the membership function and its definite integrals are involved by the method of piecewise linear approximation.And the obtained Linear Matrix Inequality(LMI)conditions are listed.Finally,through a simulation example compared with the membership independent method,employed the above information of membership function can effectively expand the stability region and reduce the existing conservatism. |
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