A new design method for continuous Takagi-Sugeno fuzzy controller with pole placement constraints: an LMI approach

A new design method for T-S fuzzy controller which guarantees global asymptotic stability and satisfies a desired performance is proposed in this paper. The method uses the LMI approach to find the common symmetric positive definite matrix P and feedback gains K_i , i=1, 2, ..., r, numerically. The LMIs for the stability criterion which treats P and K_is as matrix variables is derived from Wang et al.´s (1995) stability criterion. Wang et al.´s stability criterion uses nonlinear MIs since P and K_is are coupled together. The desired performance is represented as r LMIs which place the closed-loop poles of r local subsystems within the desired region in the s-plane. By solving the stability LMIs and pole placement constraint LMIs simultaneously, the feedback gains K_is which guarantee global asymptotic stability and satisfy the desired performance are determined. The design method is verified by designing a T-S fuzzy controller for an inverted pendulum with a cart using the proposed method