Fault Tolerant H∞ Control for a Class of Polynomial Non-linear Discrete-time Systems

This paper studies the fault tolerant control (FTC) problem for a class of polynomial nonlinear discrete-time systems with guaranteed H-infinity performance in the presence of actuator faults. The concerned fault is considered as a multi-model of the typical aberration in actuators' effectiveness. A quadratic-like polynomial Lyapunov function is presented for the H-infinity specification. The main contribution of this paper is that the effect of the nonlinear terms appear in FTC analysis is described as an index in order to transform the controller design into a semi-definite programming (SDP). A numerical example is given to verify the applicability of this new approach for the nonlinear FTC synthesis.