Linear controllers for fuzzy systems subject to unknown parameters: stability analysis and design based on linear matrix inequality (LMI) approach

This paper presents a design approach of linear controllers for nonlinear systems with unknown parameters within known bounds. The plant is represented by a fuzzy model. Stability condition will be derived based on Lyapunov stability theory and formulated into an LMI (linear matrix inequality) problem. The linear controller can be designed by solving the LMIs. To illustrate the merits and the design procedure of the proposed linear controller, an application example on stabilizing an inverted pendulum on a cart with unknown parameters is given.