Optimization study of fuzzy parametric uncertain system

Abstract

This paper deals with the analysis and design of the optimal robust controller for the fuzzy parametric uncertain system. An LTI system in which coefficients depends on parameters described by a fuzzy function is called as fuzzy parametric uncertain system. By optimal control design, we get control law and feedback gain matrix which can stabilize the system. The robust controller design is a difficult task so we go for the optimal control approach. The system can be converted into state space controllable canonical form with the α-cut property fuzzy. For optimal control design, we find control law and get the feedback gain matrix which can stabilize the system and optimizes the cost function. Stability analysis is done by using the Kharitonov theorem and Lyapunov-Popov method. The proposed method applied to a response of Continuous Stirred Tank Reactor (CSTR).