A fuzzy Lyapunov function approach for robust fuzzy control design of nonlinear systems with model uncertainties

The progress of parallel distributed control (PDC) scheme has successfully exploited the achievements of linear control theories to the fuzzy control of nonlinear systems. However, the design of control gain for each local systems dynamics is restricted by a common Lyapunov function. The lately proposed idea of fuzzy Lyapunov function is a promising analysis tool to relieve the restriction. The purpose of this paper is to remove some unnecessary constrains and complexities of the original contribution, and to extend its usability by considering model uncertainty in the closed-loop control design. In completing the design problem, all the conditions are formulated in the form of linear matrix inequalities (LMIs), which can be solved iteratively by any efficient optimization methods, such as genetic algorithms. A design and analysis example of the Lorenz system is given to illustrate the effectiveness of the proposed approach.