Quadratic stable controller design of discrete fuzzy systems

For the quadratic stable problem of discrete T-S fuzzy systems, a discrete piecewise Lyapunov function was constructed in maximal overlapped-rule groups based on the properties of fuzzy systems with two-overlapped fuzzy partition inputs. And then a new sufficient condition to check the stability of discrete closed-loop T-S fuzzy systems was proposed and proved. This condition only requires finding a common positive definite matrix in each maximal overlapped-rule group. Compared with former stability analysis approaches, this approach can not only overcome the defect of finding a common positive definite matrix but also reduce the number of solving Lyapunov inequalities. In addition, a fuzzy controller was designed to acquire global asymptotically stable fuzzy system models by means of the parallel distributed compensation approach. Finally, for a ship motion system, simulation results demonstrate that the proposed quadratic stable controller is effective.