Robust stability of mode-to-mode fuzzy controllers

An approximate method is formulated for analyzing the performance of nonlin ear systems controlled by mode-to-mode fuzzy controllers. It is assumed tha t an approximate model of the nominal plant is available and the nominal mo de-to-mode trajectory converges asymptotically from the start mode to the t arget mode of operation. Stability of the nominal mode-to-mode trajectory i n the presence of small, bounded variations of the system's parameters or t he initial conditions is considered. The method is based on formulating a p erformance measure as a Lyapunov function of the error between the nominal and perturbed mode-to-mode trajectories. The sensitivity of the deviations from the nominal mode-to-mode trajectory with respect to parametric or init ial condition variations is incorporated into the total differential of thi s performance measure. Using a Lyapunov stability condition, the robustness of the closed-loop system is analyzed by observing a definiteness conditio n of a time-varying matrix. A measure of robustness is then formulated usin g the largest singular value of a time-varying matrix. A hover mode to forw ard flight mode fuzzy controller is used to illustrate the methodology.