Fault-Tolerant Controller Design for General Polynomial-Fuzzy-Model-Based Systems

This paper studies the fault-tolerant control problem for a class of nonlinear systems based on polynomial fuzzy model. A typical actuator fault model is presented to describe the loss of effectiveness fault in a multimode framework. The considered polynomial-fuzzy-model-based systems are more general, since the assumption that the input matrix B-i(x), i = 1,..., p has at least one zero row, is not required any more. A polynomial Lyapunov function candidate depending on any system state is applied to design the fault-tolerant controller, in which the number of rules and membership functions can be matched or mismatched with polynomial fuzzy model. To deal with nonconvex problem, some nonlinear terms are successfully described as an index to be optimized to zero by a semidefinite programming. Compared with some published works, the resultant sum of squares based design conditions are with less computation complexity and potentially more relaxed. Using the third-party MATLAB toolbox SOS-TOOLS, simulation examples are given to illustrate the effectiveness of the new method.