Stabilization of Observer-based Actuator Fault-tolerant Control Systems with Uncertainties, Actuator Saturation and Disturbances: an Lmi Approach

An observer-based design method of fault-tolerant controller for uncertain linear systems subject to actuator faults, saturation and bounded disturbances is provided in this paper. A state feedback controller is designed to maximize the attraction domain with the state variables estimated by a Luenberger observer. The closed-loop system is modeled as a linear system with decentralized dead-zone nonlinearity by incorporating the state estimation errors into the state equation as new state variables. The design results for both stability and stabilization of the closed-loop system are given in the form of matrix inequalities. However, the matrix inequality conditions to compute the design parameters are non-convex in general. Then by constructing an appropriate objective function in the form of Linear Matrix Inequality (LMI), the non-convex optimization problem is converted to unconstrained nonlinear optimization problem, which can be solved by any nonlinear programming algorithm. A numerical example illustrates the effectiveness of the proposed design technique.