Robust fault-tolerant control design for polynomial fuzzy systems

Abstract

This paper focuses on the robust H∞ fault-tolerant control issue for a family of polynomial fuzzy systems subject to actuator faults and external disturbances. Especially, asynchronous fuzzy membership function technique is considered to minimize the expenses of controller implementation. To derive the robust stability conditions, actuator fault factors are taken into the account in the closed-loop system formulation. Moreover, to utilize the exact shape information of fuzzy membership functions in the stability criterion, they are approximated as sum-of-square polynomials with the aid of polynomial curve fitting method. In addition, to reduce the conservatism, a generalized polynomial Lyapunov function is considered. However, there are some non-convex terms in the stability conditions due to the construction of the generalized Lyapunov function that consists of all state-dependent polynomial matrix. Thus, some existing convex methods for general polynomial fuzzy systems are rendered inapplicable. To deal with this issue, the actual non-convex stability conditions converts into a convex optimization problem by introducing some additional convex constraints. Moreover, the membership-function-dependent robust stability conditions of the closed-loop system are provided as sum-of-square convex polynomial constraints. Lastly, the usefulness and superiority of the designed controller are illustrated by the simulation examples.