$H_2$ Control design for fuzzy dynamic systems via LMI
Ning Zhang, Gang Feng · Journal of Intelligent & Fuzzy Systems · 2000
This paper addresses the robust \(H_2\) control design of complex nonlinear systems which can be represented by a fuzzy dynamic model. Based on a continuous Lyapunov function and a piecewise continuous Lyapunov function respectively, two kinds of new control design methods are proposed using Lyapunov stability theory, robust \(H_2\) control theory and Linear Matrix Inequalities (LMI) techniques. It is shown that the closed loop fuzzy control system is asymptotically stable with a white noise attenuation. The robust \(H_2\) fuzzy controller can be obtained by using the LMI techniques. An example is given to demonstrate the application of the proposed design methods.